System and method of improved calculation of diffusely reflected light

ABSTRACT

The present invention is related to rendering computer animated video and/or images generally, and to improving the calculation of diffusely reflected light. The present invention includes a system and method of computing diffusely reflected light at one or more positions on surfaces in an object scene from object scene data. The present invention typically includes the step of and/or instructions for selecting a non-regular order for processing a plurality of positions on a surface—the plurality of positions having been predetermined. The present invention also includes the step of and/or instruction for processing the plurality of positions in the non-regular order. This processing typically includes computing diffusely reflected light at a position in the plurality of positions by reference to diffusely reflected light incident on the position when deriving the diffusely reflected light at the position by reference to diffusely reflected light at other positions computed by reference to diffusely reflected light incident on the other positions is inaccurate. Alternatively, deriving the diffusely reflected light at the position by reference to the diffusely reflected light at the other positions computed by reference to diffusely reflected light incident on the other positions when deriving the diffusely reflected light at the position by reference to the diffusely reflected light at the other positions is accurate.

RELATED APPLICATIONS

This application is related to, and incorporates herein by reference, aU.S. patent application bearing Ser. No. 09/865,990, entitled “SYSTEMAND METHOD OF LINE SAMPLING OBJECT SCENE INFORMATION,” and commonlyassigned with the present invention. This application is also relatedto, and incorporates herein by reference, a U.S. patent application Ser.No. 10/157,579 filed on May 28, 2002, entitled “SYSTEM AND METHODRELATED TO DATA STRUCTURES IN THE CONTEXT OF A COMPUTER GRAPHICSSYSTEM,” and commonly assigned with the present invention. Thisapplication is also related to, and incorporates herein by reference, aU.S. patent application Ser. No. 10/177,678 filed on Jun. 20, 2002,entitled “SYSTEM AND METHOD OF SIMULATING MOTION BLUR EFFICIENTLY,” andcommonly assigned with the present invention.

The present invention is related to rendering computer animated videoand/or images generally, and to improving the calculation of diffuselyreflected light.

BACKGROUND OF THE INVENTION

A REYES image rendering architecture is a system for computing computeranimated video or images. The details of an exemplary REYES imagerendering architecture are described in detail by Robert L. Cook, et al.in “The Reyes Image Rendering Architecture,” Computer Graphics, vol. 21,no. 4, Jul. 1987, which is incorporated herein by reference. Whenprocessed in conjunction with a REYES image rendering architecturecompatible renderer (a “REYES renderer”), primitives represent objectsthat may be included in the computer animated video or images. Theseprimitives are typically diced into polygonal meshes prior to beingshaded and projected onto an image plane. After projecting the polygonalmeshes onto the image plane, visible polygons are identified. Morespecifically, the polygons closest to defined elements of the imageplane are identified. These elements may comprise infinitesimal points,lines, or areas on the image plane. Color values computed for verticesof the visible polygons are then used to compute color values for theimage plane.

To ensure that a sufficient amount of primitive detail is included inthe computer animated video or images, each polygon in the polygonalmeshes is approximately equal in size to a pixel (e.g., the smallestdistinct area of the image plane). Computer animated video or images arerepresented by an array of numbers. In the case of a two-dimensionalimage, the array of numbers is a two-dimensional array and each numberin the array corresponds to a tiny portion of the image. Each element inthe array is referred to as a picture element (or pixel); and the pixelordinarily has the same location in the array as the portion of theimage it represents. In the case of a gray scale image, the numericalvalue of each pixel represents the relative brightness (or intensity) ofthe portion of the image to which it corresponds. In the case of a colorimage, the numerical value of each pixel is a set of numbers (or avector) representing the color of the portion of the image to which itcorresponds. Several different systems are available for numericalrepresentation of colors.

The amount of dicing applied to a primitive is, therefore, dependentupon the size of the primitive relative to a pixel. If the primitive ismuch larger, for example, a large amount of dicing may be required.Similarly, if the primitive is close in size to the pixel, a relativelysmall amount of dicing may be required.

Additionally, polygonal meshes produced by a REYES renderer areprocessed separately so that the REYES renderer need not maintain all ofthe polygonal meshes in memory or access more than just a subset of thepolygonal meshes at any one time. Because of this aspect of a REYESrenderer, color values computed for vertices do not typicallyincorporate global illumination. Persons skilled in the art recognizethat global illumination includes accounting for the effects of otherprimitives in an object scene on a vertex being shaded (e.g., accountingfor light reflected off of another primitive onto the vertex beingshaded). Instead, a REYES renderer typically shades the vertices withtexture maps and other non-global illumination techniques.

Prior art renderers that incorporate ray-tracing (“ray tracingrenderers”) trace a first set of rays (e.g., “visibility rays”) from animaginary camera or viewer's eye through a position (e.g., a pixel) onthe image plane into an object scene. The positions at which the raysintersect the object scene are visible from the image plane. Morespecifically, a position intersected by a visibility ray is visible fromthe position on the image plane through which the ray is cast.

Shading the positions at which the rays intersect the object scenetypically includes casting a set of rays (e.g., shading rays) from eachof the intersection positions. Some or all of the shading rays mayintersect other objects in the object scene. Color values computed atpositions intersected by shading rays are then used to compute colorvalues for the positions intersected by visibility rays. Ray tracingrenderers, therefore, use global illumination to compute color values.

Ray tracing renderers may also dice primitives into polygonal meshes.But polygons included in such polygonal meshes may not include polygonsapproximately equal in size to a pixel. Instead, the size of thepolygons is dependant upon, for example, the curvature of the objectmodeled by a corresponding primitive. Often times, therefore, polygonalmeshes diced from a given primitive for a ray tracing renderer are muchless complex than polygonal meshes diced from the same primitive by aREYES renderer. As the complexity of a polygonal mesh decreases, so doesthe amount of processing time required to determine whether a rayintersects the polygonal mesh.

In both REYES renderers and ray tracing renderers, the diffuseinterreflection of light among objects in an object scene may becomputed using techniques first described in detail by Gregory Ward etal. in “A Ray Tracing Solution for Diffuse Interreflection,” ComputerGraphics, Vol. 22, No. 4, August 1988, which is hereby incorporated byreference. This last technique is expanded upon by Gregory Ward and PaulHeckbert in “Irradiance Gradients,” Eurographics Rendering Workshop,May, 1992, pp. 85-98, which is also hereby incorporated by reference. Asdescribed in more detail below, these techniques include either directlycomputing diffusely reflected light at a given position in an objectscene or indirectly computing diffusely reflected light at a givenposition by reference to (e.g., averaging) diffusely reflected lightdirectly computed at neighboring positions.

In the case of ray tracing renderers, the positions for which diffuse,indirect light is computed are typically selected by the visibility rayscast from the imaginary camera or viewer's eye through positions on theimage plane. And in the case of REYES renderers, the positions for whichdiffuse, indirect light is computed are typically the vertices of thepolygonal meshes created by the REYES renderers.

As described in more detail below, when applying techniques described inthe two Gregory Ward publications listed above and other techniques forcomputing diffusely reflected light, these positions are simplyprocessed by their order of selection (e.g., as visibility rays are castinto the object scene) or by their order of storage (e.g., a row by rowin a polygonal mesh). So when indirectly computing diffusely reflectedlight at a given position, all of the other positions referenced duringthis computation typically precede the given position in terms oflocation. For example if this computation is executed for a vertex in arow of vertices on a grid of polygons, the other positions typicallyprecede the vertex in the row.

As a result, when indirectly computing diffusely reflected light at agiven position, a certain amount of extrapolation from one or moreneighboring positions, which tend to be located in a common or similardirection from the given position, is required. In other words, theseneighboring positions typically do not surround the given position.Because of this directional bias during the indirect computation ofdiffusely reflected light at the given position, increases or decreasesin the rate of change of diffusely reflected light incident on aprimitive may be missed. Similarly, diffusely reflected light at a givenset of positions that is directly computed may be marked by relativelysharp and inaccurate variations from diffusely reflected light atneighboring positions that is indirectly computed before the diffuselyreflected light at the given set of positions.

There is needed in the art, therefore, an improved technique forcomputing diffusely reflected light in an object scene. Specifically, asystem and method for improved accounting of increases or decreases inthe rate of change of diffusely reflected light.

SUMMARY OF THE INVENTION

The present invention includes a system and method of computingdiffusely reflected light at one or more positions on surfaces in anobject scene from object scene data. The present invention typicallyincludes the step of and/or instructions for selecting a non-regularorder for processing a plurality of positions on a surface—the pluralityof positions having been predetermined. The present invention alsoincludes the step of and/or instruction for processing the plurality ofpositions in the non-regular order. This processing typically includescomputing diffusely reflected light at a position in the plurality ofpositions by reference to diffusely reflected light incident on saidposition when deriving said diffusely reflected light at the position byreference to diffusely reflected light at other positions computed byreference to diffusely reflected light incident on said other positionsis inaccurate. Alternatively, deriving the diffusely reflected light atthe position by reference to the diffusely reflected light at the otherpositions computed by reference to diffusely reflected light incident onsaid other positions when said deriving the diffusely reflected light atthe position by reference to the diffusely reflected light at the otherpositions is accurate.

BRIEF DESCRIPTION OF THE DRAWINGS

Additional objects and features of the invention will be more readilyapparent from the following detailed description and appended claimswhen taken in conjunction with the drawings, in which:

FIG. 1A illustrates a computer device consistent with an embodiment ofthe present invention.

FIG. 1B illustrates the projection of an exemplary primitive on to animage plane in a manner consistent with an embodiment of the presentinvention.

FIG. 1C illustrates a grid of polygons comprising a collection ofvertices and edges.

FIG. 1D illustrates a two dimensional array for storing informationabout vertices included in a grid of polygons.

FIGS. 2A, 2B, 2C, and 2D illustrate processing steps for renderingcomputer animated video or images in a manner consistent with anembodiment of the present invention.

FIG. 3 illustrates a portion of a primitive bounding box overlapping anexemplary viewing volume.

FIG. 4 illustrates ray tracing in a simplified object scene in a mannerconsistent with an embodiment of the present invention.

FIGS. 5A and 5B illustrate problems that may arise when tracing raysinto an object scene for a finely diced grid of polygons.

FIGS. 5C, 5D, 5E, and 5F illustrate solutions, which are consistent withembodiments of the present invention, for the problems illustrated inFIGS. 5A and 5B.

FIG. 6A illustrates a problem that may arise when tracing rays into anobject scene from a primitive-edge vertex.

FIGS. 6B and 6C illustrate solutions, which are consistent withembodiments of the present invention, for the problem illustrated inFIG. 6A.

FIG. 7 illustrates processing steps for improved computation ofdiffusely reflected light in a manner consistent with an embodiment ofthe present invention.

FIG. 8 illustrates a non-regular processing order of the vertices in thegrid of polygons illustrated in FIG. 1C.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

FIG. 1A shows a computer device 100 configured to execute the variousembodiments of the present invention described below. Included in thecomputer device 100 is a central processing unit (CPU) 10, a memory 15,and i/o devices 20. The CPU 10 executes instructions as directed by theoperating system 29 and other programs maintained in the memory 15 andsends control signals to various hardware components included in thecomputer device 100. The memory 15 typically comprises high speed randomaccess memory as well as non-volatile storage such as disk storage. Inpreferred embodiments of the present invention, the memory 15 typicallyincludes object scene data 21, shaders 22, a renderer 23, a modelingapplication 25, a parser 27, an operating system 29, and active objectscene data 32.

Object scene data 21 is typically static information maintained in thenon-volatile section of the memory 15. The object scene data 21 may bemaintained in any type of data structure (e.g., database, flat filesystem, etc.) without departing from the scope of the present invention.The object scene data 21 describes one or more object scenes. An objectscene is one of many that, for example, comprise the scenes of computeranimated video. For example, object scene data 21 may describe themovement and physical or visual attributes of characters, lights, andthe environment of the object scene. In particular, and among otherthings, object scene data 21 specifies object locations and movementwithin the object scene through the use of one or more sets ofcoordinate systems. Exemplary coordinate systems are referred to asobject space, shader space, work space, camera space, screen space, andraster space. Coordinates of one system may be transformed as needed toany other coordinate system to suit a given task.

Screen space typically includes x, y, and z coordinates. The x and ycoordinates represent the horizontal and vertical positions with respectto the image plane 110 illustrated in FIG. 1B. The z coordinaterepresents a distance of, for example, an object from the image plane110. As illustrated in FIG. 1B, the image plane 110 functions as aprojection screen for primitives (e.g., models of objects) 120 includedin the object scene. Thus, the image plane 110 facilitates atransformation of three-dimensional objects to a two-dimensionalrepresentation. The image plane 110 is analogous to a monitor or videodisplay, and positions on the image plane 110 typically map to positionson a monitor or video display. Thus, references to areas of an imageplane 110 are effectively references to pixels of a monitor or videodisplay.

Object scene data 21 also includes, as noted above, information aboutthe movement of the object during a period of time associated with animage frame. This period of time is analogous to the opening and closingof a camera shutter. This information is preferably used to simulatemotion blur, which adds to the realism of computer animated video andimages. To capture object movement, object scene data 21 provides theposition of an object at the beginning of the period of time associatedwith the image frame and its trajectory and velocity during the imageframe. This permits the calculation of a position of the object duringthe period of time associated with the image frame.

As indicated above, the objects are usually modeled with primitives. Forexample, a chair may be represented by a plurality of parametric patchesor other primitives. Each of these primitives typically include physicalproperties of the objects they model. For example, a primitive thatmodels a portion of a wooden chair may be configured to interact withlight in a manner similar to that of wood.

Note that the term “primitive” used herein may refer to numerous typesof geometric primitives such as parametric quadrics, polygons,polyhedra, parametric patches (e.g., NURBS), subdivision surfaces,analytic surfaces, implicit surfaces, constructive solid geometryobjects, etc. However, certain steps described herein produce onlycertain types of primitives and certain steps described herein aretrivial for certain types of primitives, but not for others.

Shaders 22 comprise one or more programs called shaders that alsodescribe objects in the object scene. Shaders 22 are executable programsthat provide, for example, information about objects in the objectscene. Specific examples of shaders 22 include displacement shaders 22,surface shaders 22, light shaders 22, and atmosphere shaders 22. Adisplacement shader 22 typically offsets a primitive's vertices andsurface normals, which are directions perpendicular to the primitive'ssurface, to adjust the primitive's interaction with light. A surfaceshader 22 algorithmically describes the appearance of a primitive. Alight shader 22 algorithmically describes a light source. Atmosphereshaders 22 are typically used to simulate environmental conditions(e.g., fog, smoke, etc.). Other shaders 22 and shader functionality mayalso be used without departing from the scope of the present invention.

Also included in the memory 15 is the renderer 23. Renderer 23 is aprogram that processes object scene data 21, in conjunction with shaders22, to render computer animated video or images as described in detailbelow.

A modeling application 25 may create some or all of the object scenedata 21. And a parser 27 may be used by a modeling application 25 orother program to parse the object scene data 21.

The active object scene data 32 typically comprises one or moreprimitive buckets 36, one or more sample buffers 38, loaded primitivedata 40, and diffuse interreflection data 42. Like the object scene data21, the active object scene data 32 may be maintained in any type ofdata structure (e.g., database, flat file system, etc.) withoutdeparting from the scope of the present invention.

An area that corresponds to a primitive bucket 36 typically encompassesone or more pixels of a display. As described in more detail below, arenderer 23 typically processes primitives by reference to correspondingprimitive buckets 36. The use of primitive buckets 36 permits therenderer 23 to control the number of primitives that are, for example,finely and coarsely diced into grids of polygons at any one time. Aprimitive may, however, be included in more than one primitive bucket 36if it overlaps an area of the image plane 110 assigned to more than oneprimitive bucket 36. The primitive bucket 36 may take the form of anarray or linked list. Information about primitives input from the objectscene data 21 is, however, preferably maintained in the active objectscene data 32. A primitive bucket 36, therefore, is preferably comprisedof pointers to specific sections of the active object scene data 32. Therenderer 23, furthermore, preferably orders the pointers by reference tothe distance of primitives from the image plane 110. This orderingpermits the renderer 23 to, for example, efficiently cull primitivesthat are occluded by one or more other primitives closer to the imageplane 110. Despite their many advantages, primitive buckets 36 are not,however, a limitation of the present invention.

Sample buffers 38 typically include an entry for each unique spaciallocation of samples taken during the hide-visibility-grid step, which isdescribed in detail below. A sample buffer 38 typically stores a spatiallocation, one or more colors, one or more transparency values, and oneor more depth fields. This information represents a minimum amount ofdata storage for each unique spacial location (of samples) and areeventually used to compute one or more color values for each samplebuffer entry. For example, separate color values, transparency values,and depth values are maintained for each visible primitive that overlapsor is overlapped by a given sample location. Additionally, separatecolor values, transparency values, and depth values are maintained foreach instant during an object scene at which a given spatial location issampled.

As noted above, this application is related to, and incorporates hereinby reference, the U.S. patent application Ser. No. 10/157,579 filed onMay 28, 2002, entitled “SYSTEM AND METHOD RELATED TO DATA STRUCTURES INTHE CONTEXT OF A COMPUTER GRAPHICS SYSTEM,” and commonly assigned withthe present invention. This U.S. patent application describes a datastructure (e.g., a specialized sample buffer 38) optimized for storing,retrieving, and updating information in a line sampling embodiment ofthe present invention. This data structure is also within the scope ofthe present invention.

As note above, this application is related to, and incorporates hereinby reference, the U.S. patent application bearing Ser. No. 09/865,990,entitled “SYSTEM AND METHOD OF LINE SAMPLING OBJECT SCENE INFORMATION,”and commonly assigned with the present invention. This incorporated U.S.patent application describes in detail a system and method ofdistributing line samples spatially (i.e., defining spatial locations ofsamples) that is within the scope of the present invention. Othertechniques may be used for distributing samples (line samples, pointsamples, area samples, etc.) spatially without departing from the scopeof the present invention.

Loaded primitive data 40 typically includes information about primitivescopied from the object scene data 21 and information generated by therenderer 23 while processing primitives. In particular, as described inmore detail below, the present invention preferably includes thecreation of a grid of polygons for a primitive or portion of a primitivedescribed in the object scene data. A polygon typically comprises acollection of vertices connected by three or more edges. A grid ofpolygons is a collection of polygons with shared edges and vertices asillustrated in FIG. 1C. In this illustration, the grid of polygons 140consists of a five-by-five set of vertices (v142-1-v142-25). Interiorvertices are connected by four edges to four other vertices. Edgevertices are connected by two or three edges to two or three othervertices.

A grid of polygons is typically stored in, for example, a twodimensional vertices array 150 as illustrated in FIG. 1D. In thisillustration, the vertices array 150 corresponds to the grid of polygons140 illustrated in FIG. 1C, and includes an entry for each vertexincluded in the grid of polygons 140. Each entry in the vertices array150 has a plurality of fields including, for example, a spatial locationfield 152, a texture coordinates field 154, a surface normal field 156,and a direction vector field 158. The spatial location field 152typically includes the location of the corresponding vertex (typicallygiven by x, y, and z coordinates, e.g., camera space coordinates). Thetexture coordinates field 154 typically includes coordinates thatdescribe how a texture map maps onto an primitive. The surface normalfield 156 typically includes a vector that is perpendicular to aprimitive or object modeled by the primitive at the location of thecorresponding vertex. Alternatively, the vector is an average of surfacenormals for polygons that share the corresponding vertex (e.g., polygonsfor which a set of defining vertices includes the corresponding vertex).The direction vector field 158 stores a vector that is a direction to animaginary camera or viewer's eye.

Because a vertices array is stored in conjunction with a specificprimitive or portion or a primitive, the vertices array 150 need notinclude an identifier of a corresponding primitive or portion of aprimitive. Nevertheless, the vertices array 150 may include a greater orsmaller number of fields, to store more or less information, than thatwhich is illustrated in FIG. 1D without departing from the scope of thepresent invention.

The diffuse interreflection data 42 typically includes diffuseinterreflection data directly computed (e.g., by reference to objectsthat diffusely reflect light that is incident on a given position) forvertices of, or other positions on, grids of polygons created forprimitives in a given object scene. As described in more detail below,this information is generated while shading grids of polygons createdfor primitives in a given object scene in step 256 of FIG. 2A.

In some embodiments of the present invention, data included in thediffuse interreflection data 42 may be used for a plurality of objectscenes. Typically, a directive to use the diffuse interreflection data42 for a plurality of object scenes is incorporated into the objectscene data 21. If the renderer 23 is not directed to use the diffuseinterreflection data 42 for a plurality of object scenes, it isdiscarded after each object scene is rendered.

Storage of the diffuse interreflection data 42 may be accomplished witha plurality of data structures without departing from the scope of thepresent invention. However, in preferred embodiments of the presentinvention, the data structure used to store the diffuse interreflectiondata 42 is a K-D tree. A K-D tree is a data structure formultidimensional, sparse data. Vertices of, or other positions on, gridsof polygons are typically defined by x, y, and z coordinates, and arethus ideally suited for storage in a K-D tree. The diffuseinterreflection data 42 is typically sparse because diffusely reflectedlight is directly computed at only a subset of all of the vertices of,or other positions on, grids of polygons created for an object scene.Further, the vertices or other positions included in this subset are notknown in advance. A K-D tree provides an ideal means for storage,update, and retrieval of the diffuse interreflection data 42. Anexemplary technique for creating and using K-D trees is described indetail by M. de Berg, et al. in “Computational Geometry: Algorithms andApplications,” Springer, Berlin, 2000, which is hereby incorporated byreference.

An entry for a position (e.g., a vertex in or other position on a gridof polygons) in a K-D tree (e.g., the diffuse interreflection data 42)typically includes a location, the surface normal of the position, andtwo gradient values, a harmonic mean distance, and a recursion level foreach computation of diffusely reflected light at the position. Thelocation typically comprises x, y, and z coordinates for camera space.These coordinates are typically extracted from the active object scenedata 32 the first time diffusely reflected light at the position iscomputed. In the case of positions other than vertices, the coordinatesare computed at an intersection of a ray with a given primitive. Asnoted above, a surface normal is typically a vector that isperpendicular to primitive or object modeled by the primitive at theposition. Alternatively, the vector may be an average of surface normalsfor polygons that share the corresponding vertex or the surface normalof the polygon upon which a position is located.

And as described in more detail below, diffusely reflected light at agiven position may be separately computed for a plurality of recursionlevels. More specifically, when diffusely reflected light at a givenposition is directly computed, a plurality of rays are cast into theobject scene from the position. If a ray intersects a primitive in theobject scene (e.g., a grid of polygons created for the primitive)(excluding lights in the object scene), diffusely reflected light atthis intersection may be computed by casting additional rays into theobject scene from this intersection (e.g., a position on a grid ofpolygons). Because the computation of diffusely reflected light at thisintersection is secondary (e.g., provides a component of diffuselyreflected light incident on another position), a smaller number of raysmay be cast from this intersection. As a result, the computation ofdiffusely reflected light at this intersection may not be very accurate.This does not typically affect the final result of the rendering processadversely because, as noted above, this value is secondary. It ispossible, though unlikely, that a plurality of rays cast into the objectmay intersect a given position, which may or may not correspond to avertex. If, for example, the renderer 23 determines that diffuselyreflected light at the vertex must be directly computed and thatdiffusely reflected light at the vertex has already been computed for ahigher recursion level (e.g., the existing value is secondary), therenderer will not use the existing computation of diffusely reflectedlight. But if diffusely reflected light at a position has already beencomputed for a recursion level lower than that associated with asecondary ray that intersects the position, the renderer 23 will use theexisting computation of diffusely reflected light. Because the existingcomputation of diffusely reflected light is more accurate than requiredby a secondary ray, there is no harm is using this value.

Additionally, a harmonic mean distance and two gradient values arecomputed in conjunction with diffusely reflected light. The computationof the harmonic mean distance is described in detail below, but brieflythese values are dependant upon the rays cast to compute correspondingdiffusely reflected light and the contribution of each ray thereto. Morespecifically, the harmonic mean distance is the harmonic mean distanceof all of the rays cast to compute corresponding diffusely reflectedlight.

The first of the two gradients is a rotational gradient and the secondof the two gradients is a translational gradient. The rotationalgradient accounts for how diffusely reflected light at a positionchanges as the position is rotated. The translational gradient accountsfor how diffusely reflect light changes as a position is translated. Theuse of the two gradients improves the accuracy of diffusely reflectedlight indirectly computed at a given position.

Attention now turns to a detailed discussion of steps taken, inconjunction with the computer device 100, in preferred embodiments ofthe present invention to render computer animated video or images.

A first step of rendering an object scene is an initialization step(step 204, FIG. 2A). This step may include assigning areas of the imageplane 110 to primitive buckets 36 and assigning sample locations tosample buffers 38. This step may also include the renderer 23initializing the color values of sample buffers 38 to a defaultbackground color (e.g., the color black) and depths of sample buffers 38to a maximum depth value (e.g., to infinity or the greatest distancethat can be represented in the depth fields 134).

The renderer 23 then determines whether a primitive is available forprocessing (step 208). This step may include, for example, the renderer23 checking for a command from a parser 27 or modeling application 25 toprocess a primitive from the object scene data 21. In some embodiments,the parser 27 parses sections of the object scene data 21, which may be,or include, a metafile. The parser 27 typically invokes a routineexecutable by the renderer 23 depending on the particular datum in theobject scene data 21 parsed. In other embodiments, the modelingapplication 25 bypasses the parser 27, processes the object scene data21, and invokes the appropriate routine executable by the renderer 23(using, for example, an application program interface of the renderer23). Essentially, the parser 27 or the modeling application 25 mayinvoke action by the renderer 23 for each primitive included in theobject scene data 21. Additionally, the parser 27 or the modelingapplication 25 may set attributes and options applicable to a particularprimitive. These attributes and options are then applied by the renderer23 while processing the object scene data 21.

Step 208 may also included the renderer 23 scanning the object scenedata 21 and one or more primitive buckets 36 for an available primitive.A primitive is not available from the object scene data 21 if, forexample, each primitive defined by the object scene data 21 has beencopied into the active object scene data 32. Similarly, a primitive isnot available from a primitive bucket if, for example, each primitiveassigned to the primitive bucket has been culled and/or subjected to thehide-visibility-grid step.

If a primitive is not available, the renderer 23 composites and filtersdata stored in the sample buffer 38 (step 296). This step includescombining color values stored in the sample buffer 38 to form a colorvalue for each pixel that defines, for example, a display or image. Asindicated above, a plurality of color values may be maintained for asample location. Color values (in connection with transparency valuesand depth values) computed for a given sample location at differenttimes during an object scene or image frame may be combined to form asingle color value for the sample location. In preferred embodiments,color values computed at different times are weighted evenly andaveraged. Many techniques for combining color values are known in theart, all are within the scope of the present invention. These colorvalues are then output to a display or stored for subsequent use inmemory 15 (step 298).

If a primitive is available, the renderer 23 preferably selects aprimitive directly from the object scene data 21 or indirectly through aprimitive bucket 36 (step 212). In preferred embodiments of the presentinvention, the renderer 23 selects all of the primitives defined in theobject scene data 21 before selecting a primitive (indirectly) from aprimitive bucket 36. And when a primitive is selected from the objectscene data 21, the renderer 23 preferably adds some or all of the objectscene data 21 pertaining to the primitive to the active object scenedata 32. More specifically, the renderer 23 adds primitive data to theloaded primitive data 40 and assigns the primitive to one or moreprimitive buckets 36. Once assigned to a primitive bucket 36, therenderer inserts one or more pointers to the primitive data into theprimitive bucket 36.

Additionally, in some embodiments of the present invention, the renderer23 selects a current primitive bucket 36 and does not process otherprimitive buckets until no additional primitives are available from thecurrent primitive bucket. Once the current primitive bucket is depleted,a new current primitive bucket is selected.

Another complexity in this process is the possible splitting ofprimitives. As described in more detail below, a primitive may be splitsuch that a pointer included in a primitive bucket may point to only aportion of a primitive. So when an entry in a primitive bucket isselected by a renderer 23 (e.g., during step 212 described in thefollowing paragraph), the renderer 23 may be selecting a portion of aprimitive instead of an entire primitive.

After selecting a primitive or a portion of a primitive (step 212), therenderer 23 bounds the selected primitive or portion of a primitive in abounding box (step 216). Persons skilled in the art recognize that abounding box is an imaginary box (e.g., a volume) representing themaximum dimensions of a bound primitive or portion of a primitive. Thebounding box permits the renderer 23 to quickly determine whether aprimitive or portion of a primitive may occupy certain space in theobject scene. It is possible that even if the bounding box does occupythe space, a primitive or portion of a primitive bound by the boundingbox may not.

The renderer 23 may bound the selected primitive or portion of aprimitive or a representation of the selected primitive or portion of aprimitive. If, for example, the selected primitive or portion of aprimitive comprises a parametric patch, the parametric patch may bebound. Because of the nature and complexity of such parametric patches,suitable bounding boxes may not tightly follow the contours of theselected primitive or portion of a primitive. How tightly the boundingbox follows the contours of the selected primitive or portion of aprimitive is a design choice. A bounding box that tightly follows thecontours of the selected primitive or portion of a primitive typicallyrequires more processing time for creation than a bounding box that doesnot tightly follow the contours of the selected primitive or portion ofa primitive.

But as described in detail below, a primitive or portion of a primitivemay be diced into a grid of polygons (e.g., a representation of aprimitive or portion of a primitive). Because a grid of polygons is arelatively simplistic primitive, less processing time is typicallyrequired to create a bounding box for a grid of polygons than forprimitives or portions of a primitive. As a result, the bounding boxcreated in step 216 preferably bounds a grid of polygons created fromthe selected primitive or portion of a primitive when such a grid isavailable (e.g., step 244 has already been executed for the selectedprimitive or portion of a primitive).

The renderer 23 then determines whether the selected primitive orportion of a primitive is on-screen (step 220). The object scene data21, and thus the active object scene data 32, typically includes adescription of a viewing volume that contains everything that may bevisible by an imaginary camera or viewer. If no portion of the boundingbox is within this viewing volume, the selected primitive or portion ofa primitive is not on-screen. The renderer 23 typically comparescoordinates computed for the bounding box to a compatible set ofcoordinates for the viewing volume to make this determination.Additionally, when the selected primitive or portion of a primitive iswithin the viewing volume, as indicated by the bounding box, but facesaway from the imaginary camera or viewer, the selected primitive orportion of a primitive is not on-screen. The renderer 23 may make thisdetermination, for example, by computing a surface normal for theselected primitive or portion of a primitive. If the surface normalpoints away from the imaginary camera or viewer, the selected primitiveor portion of a primitive faces away from the imaginary camera orviewer. Note that some primitives merely model a surface of an object,so there is no viewable “back side” of such primitives. Primitives thatlack a viewable back-side and face away from the imaginary camera orview are not on-screen as well. Further, a primitive may not be onscreen if, for example, each sample location overlapped by the boundingbox of the primitive is overlapped by another primitive that is closerto the image plane 100 and each of these sample locations is in factoverlapped by another primitive.

In some embodiments, the renderer 23 bounds an entire primitive anddetermines whether the primitive is on-screen even when only a portionof a primitive is selected. More specifically, the renderer 23 boundsthe primitive that includes the selected portion. Note that whensubsequent portions of this primitive are selected, the renderer 23preferably does not bound and retest the entire primitive.

When a portion of a primitive that is on-screen when considered as partof the primitive may not be on-screen when considered alone. Asillustrated in FIG. 3, a portion of the bounding box 304 for a primitiveoverlaps an exemplary viewing volume 302. The primitive illustrated inFIG. 3 includes a line that marks where the primitive 120 may be splitduring the splitting step described below. The first portion of theprimitive 120, as indicated by the line, falls entirely outside of theviewing volume 302. A bounding box for the first portion of theprimitive 120 may not, therefore, overlap the viewing volume 302 afterbeing subjected to the splitting step. But the second portion of theprimitive, and any bounding box created therefore, will continue tooverlap the viewing volume 302 after being subjected to the splittingstep.

If the renderer 23 determines that the selected primitive or portion ofa primitive is not on-screen (step 220-No), the renderer 23 preferablyremoves the pointer to the selected primitive or portion of a primitivefrom the primitive buckets 36 (step 222, FIG. 2B). But if the renderer23 determines in step 220 that the primitive that includes the selectedportion is not on-screen, the renderer 23 may remove all pointers tothis primitive from the primitive buckets 36.

The renderer 23 then preferably culls corresponding visibility grids,which are described below, from the active object scene data 32 (step224). At the very least, a visibility grid created for the selectedprimitive or the selected portion of a primitive is removed. But if therenderer 23 determines in step 220 that the primitive that includes theselected portion is not on-screen, the renderer 23 may remove allvisibility grids created for this primitive.

The renderer 23 then determines whether the selected primitive orportion of a primitive is ray traceable (step 226). Note that if aprimitive is ray traceable, all of its portions are typically raytraceable as well.

If the renderer 23 determines that the selected primitive or portion ofa primitive is ray traceable (step 226-Yes), the renderer 23 returns tostep 208 to select another primitive or portion of a primitive. Sincethe selected primitive or portion of a primitive may be intersected by aray while the renderer 23 is shading another primitive, data about theselected primitive or portion of a primitive is preferably maintained.

If the renderer 23 determines that the selected primitive or portion ofa primitive is not ray traceable (step 226-No), the renderer 23 cullsthe corresponding shading grid, which is described below, from theactive object scene data 32 (step 228). This corresponding shading gridis not needed because there are no visibility grids corresponding to theselected primitive or portion of a primitive that may be shaded and thiscorresponding shading grid will not be intersected with rays to shadeother primitives or portions of a primitive.

The renderer 23 then determines whether the selected primitive or theprimitive that includes the selected portion is referenced in anyprimitive buckets 36 (step 230). If not (step 230-No), the renderer 23culls data related to the selected primitive or the primitive thatincludes the selected portion from the active object scene data 32(except, for example, an indication that the selected primitive or theprimitive that includes the selected portion has already beenprocessed)(step 231). This data is no longer needed because theprimitive will not be referenced again while processing the activeobject scene data 32. But if the selected primitive or the primitivethat includes the selected portion is referenced in any primitivebuckets 36 (step 230-Yes) or after executing step 321, the renderer 23returns to step 208 to select another primitive or portion of aprimitive.

If the selected primitive or portion of a primitive is on-screen (step220-Yes), the renderer 23 determines whether the selected primitive orportion of a primitive is too large (step 232). As described in moredetail below, primitives or portions of a primitive may be subject to aprocess commonly referred to as dicing, which typically includesdividing a primitive or portion of a primitive, such as a bicubic patch,into a grid of polygons. Often times, a large number of polygons mayresult from the dicing process. But in preferred embodiments of thepresent invention, the renderer 23 avoids concurrently processing enoughpolygons to require excessive use of slower portions of the memory 15(e.g., disk storage). Instead, the renderer 23 computes or estimates thenumber of polygons that may result from dicing the selected primitive orportion of a primitive to determine whether the selected primitive orportion of a primitive is too large.

If the selected primitive or portion of a primitive is too large (e.g.,too many polygons may result from dicing the selected primitive orportion of a primitive) (step 232-Yes), the renderer 23 splits theselected primitive or portion of a primitive (step 236). For example, ifthe selected primitive or portion of a primitive is a parametricprimitive, such as a NURBS, the renderer 23 identifies parametric linesthat divide the selected primitive into two or more smaller NURBS. Therenderer 23 then preferably deletes the entry included in the primitivebuckets 36 for the selected primitive or portion of a primitive beforethe split. This entry is replaced with separate entries for each of thetwo or more smaller NURBS. Each of these entries points to data in theloaded primitive data 40 relating to the selected primitive or theprimitive that includes the selected portion, but also identify specificportions of the selected primitive or the primitive including theselected portion. This way, any parameters, options, etc. applicable tothe selected primitive or the primitive including the selected portionare, in effect, carried over to the new entries. New entries may then beseparately processed by the renderer 23 in connection with steps 208-236until each entry, and subsequent new entries, points to a portion of aprimitive that is both on-screen and small enough for dicing.

If the selected primitive or portion of a primitive is not too large(step 232-No), the renderer 23 determines whether a finely diced or highresolution primitive (“visibility grid”) corresponding to the selectedprimitive or portion of a primitive has been created (step 240).

As noted above, dicing a primitive or portion of a primitive typicallyproduces a grid of polygons. Some grids of polygons that result fromdicing are shaded and projected onto the image plane 110. To ensure thatcomplex details of modeled objects are adequately rendered, each polygonshaded and projected onto the image plane 110 is preferably smaller thana pixel, which is the smallest indivisible unit of a monitor or displayscreen and is assigned only one color. Creating polygons of this sizepermits separate colors or color values to be computed for each pixel ofa display. And in preferred embodiments, the renderer 23 (and shaders22) computes colors or color values for each vertex that defines apolygon. So in these embodiments, four or more separate colors or colorvalues are computed and combined for each pixel.

Part of the shading process (e.g., the process of computing colorvalues) includes tracing rays for a position on a first primitive intoan object scene defined by the object scene data 21. The renderer 23then computes color values for positions on the same or other primitivesintersected by these rays (which may include tracing rays from thisposition into the object scene in an iterative process). These colorvalues are then used to compute a color value for the position on thefirst primitive.

Because the individual color values computed for primitives intersectedby rays traced for the first primitive may not, individually, have atremendous impact on the first primitive, the primitives intersectedneed not comprise a grid of polygons in which each polygon isapproximately equal in size to a pixel of a display. Additionally, colorvalues computed for primitives intersected by rays traced for the firstprimitive are computed at the position of the intersection, notsurrounding vertices. In other words, the level of detail provided byvery small polygons may not be necessary. Additionally, intersectingrays with very small polygons is a more time consuming process thanintersecting rays with larger polygons.

Instead, primitives intersected by rays preferably comprise grids ofpolygons in which each polygon is sized by reference to, for example,the curvature of the object or object portion being modeled by theprimitives. Thus, were the object is relatively flat, larger polygons(i.e., low resolution or coarsely diced grids of polygons) aresufficient. And where, the object has a high degree of curvature,smaller polygons (i.e., high resolution or finely diced grids ofpolygons) are often required to adequately represent the object. Inother words, the resolution of a primitive (e.g., a grid of polygons)created for intersecting rays is independent of the primitive's sizerelative to a pixel. Generally, even objects or object portions with ahigh degree of curvature will not require polygons smaller than the sizeof a pixel.

But as indicated above, a primitive may be on-screen (and thus shadedand projected onto the image plane 110) and ray traceable (and thuspossibly intersected with rays). As a result, some embodiments of thepresent invention include the steps of creating two primitives forobjects or object portions. A first primitive, if created, may comprisea coarsely diced grid of polygons and be used by the renderer 23 for rayintersecting and shading visibility grids. A primitive for rayintersecting may not, however, be created when a corresponding object orobject portion is defined by a relatively simple equation (e.g., asphere). The renderer 23 is able to compute ray intersections moreefficiently with such equations than with a coarsely diced grid ofpolygons. A second primitive typically comprises a finely diced grid ofpolygons and is used for shading and projection onto the image plane110. Although separate primitives are created, the renderer 23concurrently uses both primitives while rendering an object scene asdescribed in more detail below.

If a visibility grid corresponding to the selected primitive or portionof a primitive has not been created (step 240-No), the renderer 23finely dices the selected primitive or portion of a primitive to createthe visibility grid (step 244). The renderer 23 then returns to step 208to continue processing available primitives. In other words, an entryfor the selected primitive or portion of a primitive is left in one ormore primitive buckets 36 for subsequent selection by the renderer 23.In particular, the renderer 23 can create a tighter bounding box for avisibility grid than it can for a selected primitive or portion of aprimitive, as described above. So the visibility grid may indicate thatthe selected primitive or portion of a primitive is not actuallyon-screen.

Numerous dicing techniques may be used without departing from the scopeof the present invention. In one embodiment of the invention, primitivesare subjected to a subdivision rule. The details of an exemplarysubdivision rule are described in detail by E. Catmull and J. Clark in“Recursively generated B-spline surfaces on arbitrary topologicalsurfaces,” Computer-Aided Design 10(6):350-355, November 1978,incorporated herein by reference. In another embodiment, forwarddifferencing is used to evaluate the selected primitive or portion of aprimitive at a plurality of positions, which become vertices in theresulting primitive. The details of an exemplary forward differencingprocess are described in detail by Ari Rappoport in “Rendering Curvesand Surfaces with Hybrid Subdivision and Forward Differencing,” ACMTransactions on Graphics, 10(4):323-341, October 1991, incorporatedherein by reference.

As described in the references incorporated in the preceding paragraph,the creation and/or identification of vertices is governed bycoordinates and/or control points of a primitive from which a grid ofpolygons is being generated. In the case of subdivision, a simpleexample is piecewise linear subdivision wherein the x and y coordinatesof a new vertex equal ½* (x₁+x₂) and ½*(y₁+y₂) respectively, where (x₁,y₁) and (x₂, y₂) are surrounding vertices used to derive the new vertex.More complex examples are possible and within the scope of the presentinvention. The point is that the generation of vertices is deterministicand governed by an explicit set of rules. The storage of verticescreated in the subdivision process is similarly deterministic. Forexample, the vertices may be stored in order of creation. The verticesmay also be stored in different orders without departing from the scopeof the present invention.

Similarly, the generation of grids of micropolygons by forwarddifferencing is deterministic and governed by an explicit set of rules.Persons skilled in the art recognize that forward differencing is theupdating of discrete variable values by forming an expression thatincrements the discrete variable values from one value to the next(e.g., f(t+k)=f(t)+Df(t) or f_(n+1)=f_(n)+Df_(n)). The forwarddifferencing process is typically executed in each parametric domain ofa given primitive. For example, if a primitive is defined parametricallyby u and v coordinates, an initial v coordinate is selected, the ucoordinate is then evaluated at each of a defined step along the extentof the u domain. The v coordinate is then incremented, and the processof evaluating the u coordinate at each of a defined step along theextent of the u domain is repeated. The storage of vertices created witha forward differencing process is similarly deterministic. For example,the vertices are typically stored in order of creation.

If a visibility grid corresponding to the selected primitive or portionof a primitive has been created (step 240-Yes), the renderer 23determines whether a coarsely diced or low resolution primitive(“shading grid”) corresponding to the selected primitive or portion of aprimitive has been created (step 248). If not (step 248-No), therenderer 23 coarsely dices the selected primitive or portion of aprimitive to create the shading grid (step 252).

In some embodiments of the present invention, rays are cast from shadinggrids while shading a corresponding visibility grid. In theseembodiments, therefore, a shading grid is always created for primitivesor portions of a primitive on-screen. But in other embodiments of thepresent invention, a shading grid is created only if a correspondingprimitive or portion of a primitive is ray traceable. In theseembodiments, rays are cast directly from the visibility grid whileshading the visibility grid. In either embodiment, however, rays castare preferably intersected only with shading grids (note that a ray castfrom a visibility grid may intersect itself), so a shading grid may becreated for the selected primitive or portion of a primitive either way.But in the embodiments in which rays are cast directly from thevisibility grid while shading the visibility grid, the creation of acorresponding shading grid is delayed at least until it is determinedthat a ray intersects a bounding box of the selected primitive orportion of a primitive.

The renderer 23 then determines whether the visibility gridcorresponding to the selected primitive or portion of a primitive hasbeen shaded (step 254). If the visibility grid corresponding to theselected primitive or portion of a primitive has not been shaded (step254-No), the renderer 23 (and the shaders 22) shades the visibility grid(step 256). This step may include the renderer 23 evaluatingdisplacement shaders 22, surface shaders 22, light shaders 22, andatmosphere shaders 22 for the vertices of the visibility grid and theshading grid. During these evaluations, the shaders 22 may compute colorvalues, offset the positions of vertices, and/or modify the surfacenormals of primitives.

To facilitate the computation of color values, rays are cast for thevisibility grid being shaded into the object scene. Rays may be castfrom the visibility representation or a corresponding shading griddepending on the embodiment in use or instructions included in theobject scene data 21. The object scene data 21 may specify, for example,that a displacement shader is attached to a primitive and thus alwaysapplied to a corresponding visibility grid during the shading step. Theobject scene data 21 may further specify, for example, that the effectof the displacement shader is significant such that rays must be castdirectly from a visibility grid (even in embodiments that wouldotherwise cast rays from a corresponding shading grid).

FIG. 4 illustrates ray tracing in a very simplistic object scene.Included in FIG. 4 are two light sources 410, 420, six exemplary rays430, 440, 450, 460, 470, 480 a first primitive 120-1, a second primitive120-2, and a third primitive 120-3. In this illustration, a vertex ofthe first primitive 120-1 is being shaded. To do so, separate rays 430,440 are cast towards the first and second light sources 410, 420,respectively, and a ray 450 is cast (possibly randomly) into the objectscene. The first light source 410 is intersected by a ray 430, so itshines light onto the vertex being shaded (e.g., provides a color valuefor the vertex). The second light source, however, is not intersected bya ray 440. Instead, the ray 440 cast towards the second light source isblocked by the third primitive 120-3. As a result, the vertex beingshaded is in a shadow cast by the second light source 420 and the thirdprimitive 120-3 (e.g., they too provide a color value for the vertex).The third ray cast, ray 450, intersects the second primitive 120-2. Therenderer 23 (and shaders 22) responds to this intersection by castingadditional rays 460, 470, 480 from this intersection. Two of these rays460, 470 are cast towards, and intersect, the first and second lightsources 410, 420 respectively. These intersections provide color valuesfor the ray intersection on the second primitive 120-2 (e.g., the originof the rays 460, 470). A third ray, ray 480, cast from the secondprimitive 120-2 does not intersect any of the primitives illustrated inFIG. 4. When this occurs, a background color value is typically assignedto the ray (e.g., to the origin of the ray). The color values computedfor the rays 460, 470, 480 cast from the second primitive 120-2 are thenused to compute a color value for the intersection of the ray 450 castfrom the first primitive and intersected with the second primitive120-2. This color value is then used along with the color valuescomputed for the other two rays 430, 440 cast from the first primitive120-1 to compute a color value for the vertex being shaded.

Note that the rays 460, 470, 480 cast from the second primitive 120-2may be thought of as secondary rays since they are used to compute acolor value for the intersection of another ray and a primitive. Eachcolor value computed for these rays typically has less of an effect onthe vertex being shaded than, for example, the rays cast directly fromthe vertex being shaded.

Without taking certain precautions described below, problems may resultfrom tracing rays directly from a visibility representation forintersection with, for example, a shading representation (as notedabove, rays may be intersected directly with objects or object portionsdefined by a relatively simple equation). FIGS. 5A and 5B illustratetypical problems. FIG. 5A includes a light source 550 and elements of ashading grid and a visibility grid. The elements of the visibility gridare defined by vertices v 504, v 506, v 508, v 510, v 512, v 514, and v516. These vertices are connected by thin edges (e.g., edges of apolygon). A subset of these vertices, including vertices v 504, v 510,and v 516, define the elements of the shading grid and are connected bythick edges. Note that only some embodiments of the present inventionuse shading and visibility grids that share vertices.

Ray 542 is shown being projected from vertex v 508 of the visibilitygrid. The path of the ray 542 illustrated in FIG. 5A shows that the rayintersects with an edge of the shading grid. This sort of inter-objectintersection is often invalid and capable of producing perceivable imageartifacts. In this example, the ray 542 would otherwise intersect thelight source 550, which would shine light on the vertex v 508. Instead,the vertex v 508 is invalidly in the shadow of the shading grid.

FIG. 5B includes the items illustrated in FIG. 5A and elements of asecond shading grid and a second visibility grid. The elements of thesecond visibility grid are defined by vertices v 524, v 526, v 528, v530, v 532, v 534, and v 536. These vertices are connected by thin edges(e.g., edges of a polygon). A subset of these vertices, includingvertices v 524, v 530, and v 536, define the elements of the secondshading grid and are connected by thick edges.

As illustrated in FIG. 5B, the (first) visibility grid overlaps thesecond shading grid. As a result, the exemplary ray 544 cast from thevertex v 514 does not intersect the second shading grid as it should.And again, in preferred embodiments of the present invention, rays areintersected only with coarse representations of objects so the ray 544does not intersect the second visibility grid either. Because the ray544 does not intersect the second shading or visibility grid, the ray544 intersects the light source 550, which shines light on the vertex v514.

But as indicated by the second visibility grid, which is typically morerepresentative of that actual shape and position of a modeled objectthan a shading grid, the vertex v 514 should be in a shadow of theobject modeled by the second shading and visibility grids. But the lightsource 550 invalidly shines on the vertex v 514.

Embodiments of the present invention include numerous techniques foraddressing the problems illustrated in FIGS. 5A and 5B, two of which aredescribed in detail below. In one embodiment of the present invention,origins of rays, such as ray 542 and ray 544, are moved from avisibility grid to a shading grid.

FIG. 5C illustrates ray 542 after its origin is moved to four exemplarypositions on the shading grid. One position is illustrated by ray 542 a.The origin of ray 542 a, as indicated by the thin black line, is locatedat the intersection of the original ray, ray 542, and the shading grid.In some respects, this is the most accurate ray origin since ray 542 awill intersect what ray 542 would have intersected. But this is notalways possible since a shading grid and a visibility grid may notoverlap in this fashion.

Another position is illustrated by ray 542 b. The origin of ray 542 b islocated at a position on the second shading grid that is closest to thevertex v 508. A thin black line, which is perpendicular to the edgeconnecting vertices v 504 and v 510 and intersecting both the vertex v508 and the origin of ray 542 b, is included in FIG. 5C to illustratethat the origin of ray 542 b is the position on the second primitivethat is closest to the vertex v 508.

Also illustrated in FIG. 5C are rays 542 c and 542 d. These raysillustrate slight variations of the strategies discussed in thepreceding two paragraphs. The origin of ray 542 c is the vertex v 504,which is the vertex on the shading grid that is closest to the vertex v508 and the origin of the ray 542 b (the position on the shading gridclosest to the vertex v 508). The origin of ray 542 d is the vertex v510, which is the vertex of the shading grid that is closest to theintersection of the shading grid and the path of the ray 542. In certainsituations, however, mapping ray origins to vertices on a shading gridmay be problematic. Consider a situation where a primitive models alarge flat surface. A shading grid derived from such a primitive maycomprise a very small number of vertices over a relatively large area.But a visibility grid derived from such a primitive may comprise a verylarge number of vertices because of the size of the surface in relationto a pixel area. This situation may, therefore, result in imageartifacts due do a large number of ray origins being mapped to a smallnumber of vertices and the offset of the ray origins from their originalpositions being great.

FIG. 5D illustrates ray 544 after its origin is moved to four exemplarypositions on the (first) shading grid. One position is illustrated byray 544 a. The origin of ray 544 a, as indicated by the thin black line,is located at the intersection of the ray 544 (if traced towards thefirst shading grid) and the first shading grid.

Another position is illustrated by ray 544 b. The origin of ray 544 b islocated at a position on the first shading grid that is closest to thevertex v 514. A thin black line, which is perpendicular to the edgeconnecting vertices v 510 and v 516 and intersects both the vertex v 514and the origin of ray 544 b, is included in FIG. 5D to illustrate thatthe origin of ray 544 b is the position on the first shading gridclosest to the vertex v 514.

Also illustrated in FIG. 5D are rays 544 c and 544 d. These raysillustrate slight variations of the strategies discussed in thepreceding two paragraphs. The origin of ray 544 c is the vertex v 510,which is the vertex on the first shading grid that is closest to thevertex v 514 and the origin of the ray 544 b (the position on the firstshading grid closest to the vertex v 514). The origin of ray 544 d isthe vertex v 516, which is the vertex on the first shading grid that isclosest to the intersection of the shading grid and the path of the ray544 (if traced towards the first shading grid).

As a result of the ray origin shifting illustrated in FIGS. 5C and 5D,the ray 542 will not invalidly intersect the first shading grid and theray 544 will not invalidly bypass the second shading grid. While thesetechniques may introduce a certain amount of inaccuracy into a resultingimage, they provide an improvement over prior art since any suchinaccuracy is less than that caused by invalid inter-objectintersections.

In preferred embodiments, parameters of parametrically definedprimitives (e.g., NURBS) are used to compute positions on shading gridscorresponding to vertices of visibility grids. When a primitive isdefined parametrically, the vertices of a corresponding visibility gridand a corresponding shading grid include parameters associated with aspecific position on the primitive. Consider the illustration of FIG.5E, which includes the curved surface of primitive 560 (thinnest line),a visibility grid 562 corresponding to the primitive 560, a shading grid564 (thickest lines) corresponding to the primitive 560, vertices v 570,v 571, v 572, v 573, v 574, v 575, v 576, position p 577, and position p578. As indicated in FIG. 5E, vertices v 570, v 571, v 572, v 573, v574, v 575, and v 576 have exemplary parametric values equal to 0, ⅓, ⅔,1, {fraction (1/10)}, {fraction (4/10)}, and {fraction (9/10)}respectively. Additionally, vertices v 570, v 571, v 572, and v 573define the visibility grid 562 and vertices v 574, v 575, and v 576define the shading grid 564. The parametric values are derived from acommon source, the primitive 560, so these values are used to computepositions on the shading grid 564 that correspond to positions (e.g.,vertices) on the visibility grid 562.

To compute, for example, a position on the shading grid 564 thatcorresponds to the vertex v 571, the renderer 23 first locates verticeson the shading grid 564 that encompass the parametric value of vertex v571. As noted above, vertex v 571 has a parametric value of ⅓. Verticesv 574 and v 575, therefore, encompass vertex v 571. The equation forcomputing the corresponding position is as follows p=(t-t0)/(t1-t0),where t is the parametric value of the vertex (or other position) on thevisibility grid, t0 is the parametric value of a first of two verticeson the shading grid that encompass parametrically the vertex on thevisibility grid, t1 is the parametric value of a second of two verticeson the shading grid that encompass parametrically the vertex on thevisibility grid, and p is the position on the edge or line connectingthe two vertices on the shading grid that encompass parametrically thevertex on the visibility grid. In this example, p=(⅓-{fraction(1/10)})/({fraction (4/10)}-{fraction (1/10)})={fraction (7/9)}. Theposition p 577 on the edge or line that connects vertices v 574 and v575 illustrates the result of this calculation.

To compute, for example, a position on the shading grid 564 thatcorresponds to the vertex v 572, the renderer 23 first locates verticeson the shading grid 564 that encompass the parametric value of vertex v572. As noted above, vertex v 572 has a parametric value of ⅔. Verticesv 575 and v 576, therefore, encompass vertex v 572. The equation forcomputing the corresponding position is again p=(t-t0)/(t1-t0). In thisexample, p=(⅔-{fraction (4/10)})/({fraction (9/10)}-{fraction(4/10)})={fraction (8/15)}. The position p 578 on the edge or line thatconnects vertices v 575 and v 576 illustrates the result of thiscalculation.

FIG. 5F illustrates an extension of the technique illustrated in FIG. 5Eto two dimensions. FIG. 5F includes a visibility grid 580, a shadinggrid 582, vertex v 584, which is located on the visibility grid 580, andvertices v 586, v 588, v 590, and v 592, which are located on theshading grid 582. The visibility grid 580 and the shading grid 582 inthis illustration were computed from a common primitive, but thevisibility grid 580 includes more vertices, edges, polygons, etc. Inother words, the shading grid 582 has a coarser resolution than thevisibility grid 580.

In a preferred embodiment, reference is made to two parametric values(e.g., one value for each dimension) (arbitrarily named u and v)associated with the vertex v 584. The specific parametric valuesassociated with the vertex v 584 are (u′, v′).

The renderer 23 preferably locates four vertices on the shading grid 582that encompass the vertex v 584 parametrically. More specifically, thefour vertices the form the smallest polygon that encompasses or overlapsthe vertex v 584. In this illustration, these vertices are identified asv 586, v 588, v 590, and v 592. Parametric values (u₀, v₀), (u₀, v₁),(u₁, v₀), and (u₁, v₁) are associated with vertices v 586, v 588, v 590,and v 592, respectively. Each of these vertices also has an associatedposition within the object scene. Preferably, the position is given byx, y, and z coordinates (e.g., camera space coordinates).

The actual values of the parametric values (i.e., (u′, v′), (u₀, v₀),(u₀, v₁), (u₁, v₀), and (u₁, v₁)) are irrelevant for purposes ofillustration. Suffice it to say that u′ is greater than u₀, but lessthan u₁ and v′ is greater than v₀, but less than v₁. Locating verticeson the shading grid 582 that meet this requirement, in connection with avertex on the visibility grid 580, is a trivial operation and completedby analysis of active object scene data 32 corresponding to theprimitive represented by the shading grid 582 and visibility grid 580.

After locating the four vertices (e.g., v 586, v 588, v 590, and v 592),weights for each coordinate that defines the position of the fourvertices in the object scene are computed by reference to the parametricvalues of the vertex v 584 (e.g., (u′, v′)) and the four vertices (e.g.,(u′, v′), (u₀, v₀), (u₀, v₁), (u₁, v₀)) using the following equations:${pu} = {{\frac{u^{\prime} - u_{0}}{u_{1} - u_{0}}\quad{and}\quad{pv}} = {\frac{v^{\prime} - v_{0}}{v_{1} - v_{0}}.}}$

As noted above, each of the four vertices v 586, v 588, v 590, and v 592preferably has an x, y, and z coordinate. Corresponding coordinates fromeach of these vertices are weighted by the pu and pv values, and thencombined to form a coordinate for a position on the shading grid 582that corresponds to the vertex v 584. The following equations arepreferably used for this computation:x=(1-pu)*(1-pv)*x _(v 586) +pu*(1-pv)*x _(v 590)+(1-pu)*pv*x _(v 588)+pu*px*x _(v 590)y=(1-pu)*(1-pv)*y _(v 586) +pu*(1-pv)*y _(v 590)+(1-pu)*pv*y ₅₈₈+pu*pv*y _(v 590)z=(1-pu)*(1-pv)*z _(v 586) +pu*(1-pv)*z _(v 590)+(1-pu)*pv*z _(v 588)+pu*pv*z _(v 590)

The above three equations use a particular bilinear interpolation, butother techniques are possible and within the scope of the presentinvention.

Another embodiment that addresses the problems illustrated in FIGS. 5Aand 5B includes the use of bounding boxes to ensure that two objects donot overlap before using a shading grid to intersect rays. Morespecifically, after a ray is cast from a vertex of a visibility grid,the renderer 23 executes hit tests for each shading grid in the generalarea of the ray's path. As noted above, such rays preferably intersectonly shading grids. But in this embodiment of the present invention,visibility grids are used to perform hit tests if a bounding box of theshading grid overlaps a bounding box of the visibility grid from which aray is cast. With respect to FIG. 5A, the renderer 23 trivially rejectsthe shading grid and does not use it to perform a hit test. With respectto FIG. 5B, the second shading grid overlaps the visibility grid of thefirst object, so the bounding boxes of these primitives will alsooverlap and the renderer 23 will use the second visibility grid toperform a hit test in conjunction with the ray 544. As a result, the ray544 does not invalidly bypass the object modeled by the second shadingand visibility grids.

Embodiments of the present invention also address a problem that oftenoccurs when casting rays from vertices of primitives (either visibilitygrids or shading grids). In prior art REYES architectures, and in someembodiments of the present invention, primitives are shaded withoutinformation about the locations of other primitives. As a result, rayscast from a primitive may enter invalid object scene space 612 (FIG.6A). FIG. 6A is illustrative of this problem and includes a side-view oftwo flat, perpendicular primitives 120 (i.e., the first and secondprimitive) that abut each other along a common edge that includes theprimitive-edge vertex designated 606, a set of rays 608 cast from theprimitive-edge vertex 606, valid object scene space 610, and invalidobject scene space 612. In this example, the two primitives 120 modelthe surface a common object. The space to the right of the twoprimitives 120 is an interior cavity of the common object and shouldnot, therefore, be checked for possible sources of direct and indirectlight for the primitive-edge vertex 606.

But since the renderer 23 does not typically have information about thelocation of the second primitive, the renderer 23 may cast rays directlyinto the invalid object scene space 612, as illustrated in FIG. 6A,while shading the primitive-edge vertex 606 for the first primitive.Such rays typically return color values that produce invalid shadowsalong edges of a primitive.

To avoid this problem, the renderer 23 preferably offsets the origin ofthe set of rays 608 so that the rays 608 can not be cast directly intothe invalid object scene space 612. Any direction that will not resultin a ray being invalidly cast through the surface of the first primitivewill also not result in a ray being cast directly into the invalidobject scene space 612.

FIGS. 6B and 6C illustrate ray origin shifting. FIG. 6B illustrates aresult of shifting the origin of the rays 608 illustrated in FIG. 6Aaway from the primitive-edge vertex 606. In this particular example,each ray origin is shifted to the same location. This is not, however, alimitation of the present invention. In some embodiments, one or more ofthe rays may be shifted to a unique location. FIG. 6C illustrate thegeneral direction that ray origins are shifted for a primitive comprisedof six polygons in an embodiment of the present invention.

The amount by which the rays are shifted can be determined in a numberof ways without departing from the scope of the present invention. Insome embodiments, for example, the amount may be fixed for all rayorigins shifted (even though the direction of the shift may vary foreach ray). In other embodiments, the amount of a shift is a function ofa distance between the primitive-edge vertex and surrounding vertices.

As noted above, rays are used to determine light that shines on aprimitive. Colors or color values computed for the vertices of aprimitive are then combined to form a color value for the entireprimitive.

In some embodiments, the color values computed for the vertices arebilinearly interpolated to form a color value for primitives. Personsskilled in the art recognize that interpolation is the process ofdetermining plausible in-between values by reference to explicit valuesat particular points. Linear means that the values fall along a linefrom one known point to the next. This means the value changes a fixedamount for a fixed-sized step. Bi-linear means this process is carriedout in two dimensions.

However, the light detected by the rays 608 in FIG. 6B does notcorrespond precisely to the light that actually falls on theprimitive-edge vertex 606. So in some embodiments, the location of thenew ray origin for the rays 608 is an input to the bi-linearinterpolation process described above. In still other embodiments, othervertices of the primitive are used in conjunction with the location of anew ray origin for the rays 608 to extrapolate a color value for theprimitive-edge vertex 606. In yet another embodiment, the light energydetected by the rays 608 is treated as if it were detected by rays withan origin at the primitive-edge vertex 606.

As noted above, surface shaders algorithmically describe the appearanceof a primitive. This may include accounting for direct and indirect(i.e. reflected) light that shines on a primitive and how this lightappears to an imaginary camera or viewer. Direct lighting is lightproduced by a light source that shines directly onto a primitive.Indirect lighting is light produced by a light source that is firstreflected off of, or refracted through, another primitive before itshines on a primitive. And again, obtaining this information typicallyincludes casting rays from given vertex into an object scene.

The surface of an object (and thus the primitive that models it)typically has both diffuse and specular components. As a result, bothcomponents should be accounted for when considering the interaction oflight with a primitive. Persons skilled in the art recognize that lightthat strikes a primitive with a diffuse component is scattered equallyin all directions by the diffuse component. The intensity of thereflected light is proportional to the cosine of the angle between thedirection of the light that strikes the primitive and the primitive'ssurface normal. Specular components of a primitive, such as plastic, areresponsible for shiny highlights. The intensity of light reflected byspecular components of a surface is proportional to the cosine of theangle between the direction of the specular reflection and the directionof the light that strikes the primitive.

In some embodiments of the present invention, the intensity of directlight reflected by specular components of a primitive viewed from aspecific direction is given by the following equation:I _(ds)=(ks*lp/(d*d))*(L●R)^(n),

-   -   where I_(ds) is the intensity of direct light specularly        reflected by the primitive;    -   where ks is the primitive's diffuse coefficient of reflection;    -   where lp is the intensity of the light source shining on the        primitive;    -   where d is a distance from the primitive to the light source;    -   where L is the direction to the light source;    -   where R is the direction of specular reflection; and    -   where n an approximated factor that approaches one for dull        surfaces and infinity for shiny surfaces.

In some embodiments of the present invention, the intensity of indirectlight reflected by specular components of a primitive is given by thefollowing equation:I _(is) =Kr*R+Kt*T,

-   -   where I_(is) is the intensity of indirect light specularly        reflected by the primitive;    -   where Kr is the primitive's specular coefficient of reflection;    -   where R is the intensity of light computed for a (reflection)        ray cast from the primitive;    -   where Kt is the primitive's specular coefficient of refraction;        and    -   where T is the intensity of light computed for a (refraction)        ray cast from the primitive.

In some embodiments of the present invention, the intensity of directlight reflected by diffuse components of a primitive is given by thefollowing equation:I _(dd)=(kd*lp/(d*d))*N●L,

-   -   where I_(dd) is the intensity of direct light diffusely        reflected by the primitive    -   where kd is the primitive's diffuse coefficient of reflection;    -   where lp is the intensity of the light source shining on the        primitive;    -   where d is a distance from the primitive to the light source;    -   where N is the primitive's surface normal; and    -   where L is the direction to the light source shining on the        primitive.

In some embodiments of the present invention, the intensity of indirectlight reflected by diffuse components of a primitive is given by thefollowing equation:I_(id)=ka*la,

-   -   where I_(dd) is the intensity of indirect light diffusely        reflected by the primitive    -   where ka is the primitive's diffuse coefficient of reflection;        and    -   where la is the intensity of ambient light.

As noted above, the present invention includes an improvement over priorart techniques for computing diffusely reflected light at a givenposition. As noted above, exemplary prior art techniques are describedin detail by Gregory Ward et al. in “A Ray Tracing Solution for DiffuseInterreflection,” Computer Graphics, Vol. 22, No. 4, August 1988, and byGregory Ward and Paul Heckbert in “Irradiance Gradients,” EurographicsRendering Workshop, May, 1992, pp. 85-98, which are both herebyincorporated by reference.

Referring to FIG. 7, there are shown processing steps for an improvedtechnique for computing diffusely reflected light (e.g., diffuseinterreflection, color values, or ambient light) in a manner consistentwith a preferred embodiment of the present invention. In a firstprocessing step, the renderer 23 shuffles the vertices of a gridcorresponding to the selected primitive or portion of a primitive (e.g.,a shading grid or visibility grid depending on the particular embodimentused) (step 710). Typically, this includes initializing the entries of a“shuffle” array to the position of a given entry in the array (e.g., thefifth entry in the array is set to five, etc.). The shuffle arrayincludes an entry for each of the vertices of the grid corresponding tothe selected primitive or portion of a primitive. The renderer 23 thenpreferably executes a small for loop as follows:

FOR J = 1 TO N { OTHER = RANDOM WHOLE NUMBER BETWEEN 1 AND N; SWAPSHUFFLE[J] AND SHUFFLE[OTHER]; }

In this exemplary for loop, N is equal to the number of verticesincluded in the grid corresponding to the selected primitive or portionof a primitive. Finally, the swap statement exchanges the value of the jentry with the value of the other entry. The result of this for loop isa non-regular (e.g., a random, pseudo-random, or quasi-random)processing order. Subsequent use of the shuffle array is described belowin connection with step 714. The for loop illustrated above is forillustration. A non-regular processing order may be generated in anynumber of ways without departing from the scope of the presentinvention.

Persons skilled in the art recognize that a random processing order isnon-deterministic. A pseudo-random processing order is similar to arandom processing order, but includes patterns that repeat. Aquasi-random processing order is by definition not random. Instead, aquasi-random processing order is uniformly distributed but has certainqualities in common with a random and/or pseudo-random processing order.

Some embodiments of the present invention include pseudo-random and/orquasi-random sequences of numbers in memory 15 to facilitate thecreation of a pseudo-random and/or quasi-random processing order,respectively. In these embodiments, renderer 23 steps through one ofthese sequences of numbers maintained in memory 15 when, for example,generating the other number as illustrated in the for loop above. Inthese embodiments, the other number may be generated, for example, bymultiplying a number from one of these sequences by N. If the value ofthe other number has already been selected, it is discarded an anothernumber is selected. This process in then continued until the numbers 1through N are selected.

After shuffling the vertices of the grid, the renderer directly orindirectly computes diffusely reflected light at each vertex of the grid(step 714). Directly computing diffusely reflected light includescasting a plurality of rays into the object scene from a vertex or otherposition to determine diffusely reflected light incident on the vertexor other position (e.g., ambient light) (rays that intersect lights inthe object scene are discarded or avoided). Indirectly computingdiffusely reflected light typically includes averaging diffuselyreflected light directly computed at one or more surrounding vertices orother positions.

As indicated above, the vertices of the grid are shuffled such that thevertices of the grid are processed in a non-regular order. In the forloop illustrated above, a shuffle array is created. This shuffle arrayis used in step 714 and subsequent steps to control the processing orderof the vertices (e.g., to make sure that the vertices of the grid areprocessed in a non-regular order). For example, the renderer 23 mayexecute another for loop, with an iteration of the for loop for each ofthe vertices of the grid. The renderer 23 typically starts at the firstentry of the shuffle array and processes the vertex identified by thecontents of the first entry. For example, if the value of the firstentry is five, the fifth entry in the vertices array 150 is selected forprocessing by the renderer 23. The renderer 23 then steps through theshuffle array, processing identified vertices along the way.

In a next step, the renderer 23 determines whether diffusely reflectedlight at one or more surrounding vertices or other positions within adistance that is, for example, one eighth of a predefined constant froma vertex selected in step 714 (i.e., the selected vertex) has beendirectly computed (step 718). As described above, diffuseinterreflection data 42 is preferably stored in a K-D tree. The renderer23 extracts the location of the selected vertex from the vertices array150 and uses it to scan the K-D tree for entries (e.g., vertices orother positions at which diffusely reflected light has been directlycomputed) that are within a distance that is one eighth of thepredefined constant from the selected vertex. The predefined constant istypically included in the object scene data 21, and represents a maximumdistance the renderer 23 should scan. To avoid the identification of anunnecessarily large number of vertices or other positions, the renderer23 preferably scans just a portion of this distance initially (e.g., oneeighth of the distance), and increases this portion as needed until thefull distance is scanned. In the embodiment illustrated in FIG. 7, thisinitial portion is one eighth, but other initial (and subsequent)portions may be used without departing from the scope of the presentinvention. Often times, a small number of vertices or other positionsthat are close to the selected vertex are sufficient for indirectlycomputing diffusely reflected light at the selected vertex. Using asmaller number of vertices or other positions for indirect computationof diffusely reflected light is faster. The use of an error valueensures that increased speed does not lead to unduly inaccuratecomputations.

Note that the diffuse interreflection data 42 includes diffuselyreflected light directly computed for grids previously processed inconjunction with the selected or other primitive or portion of aprimitive during the current or previous object scene. In other words,the vertices or other positions that may be within a distance that isone eighth (or other portion) of the predefined constant from theselected vertex may include vertices or other positions in addition tothose included in the grid created for the selected primitive or portionof a primitive. Similarly, other grids may share one or more of thevertices or other positions located along the edges of the grid createdfor the selected primitive or portion of a primitive.

If the renderer 23 determines that diffusely reflected light at one ormore surrounding vertices or other positions within a distance that isone eighth of the predefined constant from the selected vertex has beendirectly computed (step 718-Yes), the renderer 23 computes an errorvalue for these vertices or other positions (step 722). Whetherdiffusely reflected light directly computed at a first vertex or otherposition may be used to suitably approximate the diffusely reflectedlight actually incident on a second vertex or other position dependsupon the surface normals of the two vertices or other positions, thedistance between the two vertices or other positions, and the length ofthe rays used to directly compute the diffusely reflected light at thefirst vertex or other position. If, for example, the two vertices orother positions face opposite directions, it is likely that diffuselyreflected light directly computed at the first vertex or other positionis less suitable for approximating the diffusely reflected lightactually incident on the second vertex or other position. In thisexample, the diffusely reflected light incident on the two vertices orother positions may be very different. Additionally, as the distancebetween the two vertices or other positions increases, so does thelikelihood that the diffusely reflected light incident on the twovertices or other positions may be very different such that diffuselyreflected light directly computed at the first vertex or other positionis less suitable for approximating the diffusely reflected lightactually incident on the second vertex or other position. Finally, asthe harmonic mean distance or other mean distance (e.g., arithmetic meandistance) of the rays used to directly compute diffusely reflected lightat the first vertex or other position increases, so does the likelihoodthat diffusely reflected light directly computed at the first vertex orother position is less suitable for approximating the diffuselyreflected light actually incident on the second vertex or otherposition. The computation of the harmonic mean distance is describedbelow in connection with step 766.

To compute the error value of the diffusely reflected light computed ata given vertex or other position (i.e., the error value of the givenvertex or other positions) with respect to the selected vertex, thefollowing equation is preferably used:${ɛ_{1} = {\frac{{\overset{\rightarrow}{P} - {\overset{\rightarrow}{P}}_{1}}}{R_{1}} + \sqrt{1 - {\hat{n} \cdot {\hat{n}}_{1}}}}},$

-   -   where ε₁ is the error value corresponding to the diffusely        reflected light directly computed at the given vertex or other        position,    -   where {right arrow over (P)} is a location of the selected        vertex,    -   where {right arrow over (P)}₁ is a location of the given vertex        or other position,    -   where R₁ is the harmonic mean distance of rays cast from the        given vertex or other position,    -   where {circumflex over (n)} is the surface normal of the        selected vertex, and    -   where {circumflex over (n)}₁ is the surface normal of the given        vertex or other position.

If more than one vertex or other position is located in step 718, anerror value is computed for the diffusely reflected light directlycomputed at each of these vertices or other positions as a group.Preferably, the following equation is used to accomplish this task:$ɛ = \frac{\sum\limits_{i = 1}^{n}\quad ɛ_{i}}{n}$

-   -   where ε is the error value corresponding to the diffusely        reflected light directly computed at each of these vertices or        other positions as a group,    -   where n is a count of the one or more vertices or other        positions located in step 718, and    -   where ε_(l) is the error value computed for the diffusely        reflected light directly computed at the i^(th) vertex or other        position in the one or more vertices or other positions located        in step 718.

After computing the error value for the one or more vertices or otherpositions located in step 718, the renderer 23 determines whether theerror value is acceptable (step 726). In preferred embodiments, thisdetermination is made by reference to a predefined error toleranceincluded in the object scene data 21 and/or the active object scene data32. If the error value computed in step 722 is less than this predefinederror tolerance, the error value is acceptable.

In some embodiments of the present invention, the predefined errortolerance is adjusted by reference to the count of vertices or otherpositions located in step 718. More specifically, as the count ofvertices or other positions increases, the predefined error tolerance isincreased so that higher error values are acceptable. The principle atwork in these embodiments is that higher error values computed forindividual vertices or other positions become acceptable as the count ofvertices or other positions increases.

If the error value computed for the one or more vertices or otherpositions located in step 718 is acceptable (step 726-Yes), the renderer23 computes diffusely reflected light indirectly at the selected vertex(step 770). Typically, the result of this computation is a weightedaverage of the diffusely reflected light directly computed at the one ormore vertices or other positions located in step 718. In preferredembodiments of the present invention, this computation is very similarto computing the error value. Again, reference is made to the surfacenormals of the two vertices or other positions, the distance between thetwo vertices or other positions, and the length of the rays used todirectly compute the diffusely reflected light to weight the diffuselyreflected light. But additionally, the renderer 23 references the twogradients stored in conjunction with the diffusely reflected lightindirectly computed at the one or more vertices or other positionslocated in step 718 to perform this weighting. In particular, thefollowing equation is preferably used:$E = {\sum\limits_{i\Rightarrow 1}^{n}\quad{ɛ_{i}{\sum\limits_{i\Rightarrow 1}^{n}\frac{{{{E_{i}\left( {{\hat{n}}_{i} \times \hat{n}} \right)} \cdot {\overset{\rightarrow}{V}}_{r}}E_{i}} + {{\left( {\overset{\rightarrow}{P} - {\overset{\rightarrow}{P}}_{i}} \right) \cdot {\overset{\rightarrow}{V}}_{t}}E_{i}}}{ɛ_{i}}}}}$

-   -   where E is the diffusely reflected light indirectly computed at        the selected vertex,    -   where ε_(i) is the error value computed for the diffusely        reflected light directly computed at the i^(th) vertex or other        position in the one or more vertices or other positions located        in step 718,    -   where n is a count of the one or more vertices or other        positions located in step 718,    -   where E₁ is the diffusely reflected light directly computed at        the i^(th) vertex or other position in the one or more vertices        or other positions located in step 718,    -   where {right arrow over (V)}_(r) is the rotational gradient        computed in conjunction with E_(l),    -   where {right arrow over (V)}_(t) is the translation gradient        computed in conjunction with E_(i),    -   where {right arrow over (P)} is a location of the selected        vertex,    -   where {right arrow over (P)}_(l) is a location of the i^(th)        vertex or other position in the one or more vertices or other        positions located in step 718,    -   where {circumflex over (n)} is the surface normal of the        selected vertex, and    -   where {circumflex over (n)}_(l) is the surface normal of the        i^(th) vertex or other position in the one or more vertices or        other positions located in step 718.

If the error value computed for the one or more vertices or otherpositions located in step 718 is unacceptable (step 726-No) or if novertices or other positions are located in step 718 (step 718-No), therenderer 23 determines whether diffusely reflected light has beendirectly computed at one or more surrounding vertices or other positionswithin a distance that is, for example, one fourth of the predefinedconstant from the selected vertex (step 730). Like step 718 describedabove, the renderer 23 extracts the location of the selected vertex fromthe vertices array 150 and uses it to scan the K-D tree for entries thatare within a distance that is one fourth of the predefined constant fromthe selected vertex. Because no vertices or other positions were locatedin step 718 or the error value computed in connection with vertices orother positions that were located are not acceptable, the renderer 23preferably expands the search volume (e.g., expands the volume withinwhich the renderer 23 searches for vertices or other positions). Inpreferred embodiments of the present invention, vertices or otherpositions located in step 718 do not count towards the one or morevertices or other positions, if any, located in step 730. In otherwords, the renderer 23 must identify at least one vertex or otherposition not located in step 718 to advance to step 734.

If the renderer 23 determines that diffusely reflected light has beendirectly computed at one or more surrounding vertices or other positionswithin a distance that is one fourth of the predefined constant from theselected vertex (step 730-Yes), the renderer 23 computes an error valuefor these vertices or other positions (step 734). Step 734 isessentially identical to step 722, except that the renderer 23preferably does not re-compute error values for vertices or otherpositions, if any, located in step 718. Instead, the renderer 23preferably maintains the error values computed for these vertices orother positions in step 722 for subsequent use in steps 734, 746, andstep 758, if need be. The renderer 23 preferably uses the followingequation to compute the error value if only one vertex or other positionin total is located in step 718 and step 730:${ɛ_{1} = {\frac{{\overset{\rightarrow}{P} - {\overset{\rightarrow}{P}}_{1}}}{R_{1}} + \sqrt{1 - {\hat{n} \cdot {\hat{n}}_{1}}}}},$

-   -   where ε₁ is the error value corresponding to the diffusely        reflected light directly computed at the given vertex or other        position,    -   where {right arrow over (P)} is a location of the selected        vertex,    -   where {right arrow over (P)}₁ is a location of the given vertex        or other position,    -   where R₁ is the harmonic mean distance of rays cast from the        given vertex or other position,    -   where {circumflex over (n)} is the surface normal of the        selected vertex, and    -   where {circumflex over (n)}₁ is the surface normal of the given        vertex or other position.

And the renderer 23 preferably uses the following equation to computethe error value if more than one vertex or other position is located instep 718 and/or step 730:$ɛ = \frac{\sum\limits_{i = 1}^{n}\quad ɛ_{i}}{n}$

-   -   where ε is the error value corresponding to the diffusely        reflected light directly computed at each of these vertices or        other positions as a group,    -   where n is a count of the one or more vertices or other        positions located in step 718 and/or step 730, and    -   where ε_(i) is the error value computed for the diffusely        reflected light directly computed at the i^(th) vertex or other        position in the one or more vertices or other positions located        in step 718 and/or step 730.

After computing the error value for the one or more vertices or otherpositions located in step 718 and/or step 730, the renderer 23determines whether the error value is acceptable (step 738). The actionsof the renderer 23 in step 738 are essentially identical to those ofstep 726. In preferred embodiments, this determination is again made byreference to the predefined error tolerance included in the object scenedata and/or the active object scene data 32. If the error value computedin step 722 is less than this predefined error tolerance, which may beincreased by reference to the count of located vertices or otherpositions, the error value is acceptable.

If the error value computed for the one or more vertices or otherpositions located in step 718 and/or step 730 is acceptable (step738-Yes), the renderer 23 computes diffusely reflected light indirectlyat the selected vertex (step 770) as described above.

If the error value computed for the one or more vertices or otherpositions located in step 718 and/or step 730 is unacceptable (step738-No) or if no vertices or other positions are located in step 718 andstep 730 (step 718-No, step 730-No), the renderer 23 determines whetherdiffusely reflected light has been directly computed at one or moresurrounding vertices or other positions within a distance that is, forexample, one half of the predefined constant from the selected vertex(step 742). The renderer 23 extracts the location of the selected vertexfrom the vertices array 150 and uses it to scan the K-D tree for entriesthat are within a distance that is one half of the predefined constantfrom the selected vertex. If no vertices or other positions were locatedin step 718 and step 730 or the error value computed in connection withvertices or other positions that were located is unacceptable, therenderer 23 preferably expands the search volume. In preferredembodiments of the present invention, vertices or other positionslocated in step 718 and/or step 730 do not count towards the one or morevertices or other positions, if any, located in step 742.

If the renderer 23 determines that diffusely reflected light has beendirectly computed at one or more surrounding vertices or other positionswithin a distance that is one half of the predefined constant from theselected vertex (step 742-Yes), the renderer 23 computes an error valuefor these vertices or other positions (step 746). Step 746 isessentially identical to step 722 and step 734, except that the renderer23 preferably does not re-compute error values for vertices or otherpositions, if any, located in step 718 and/or step 730. Instead, therenderer 23 preferably maintains the error values computed for thesevertices or other positions in step 722 and/or step 734 for subsequentuse in steps 746 and 758, if need be. The renderer 23 preferably usesthe following equation to compute the error value if only one vertex orother position in total is located in step 718, step 730, and step 742:${ɛ_{1} = {\frac{{\overset{\rightarrow}{P} - {\overset{\rightarrow}{P}}_{1}}}{R_{1}} + \sqrt{1 - {\hat{n} \cdot {\hat{n}}_{1}}}}},$

-   -   where ε₁ is the error value corresponding to the diffusely        reflected light directly computed at the given vertex or other        position,    -   where {right arrow over (P)} is a location of the selected        vertex,    -   where {right arrow over (P)}₁ is a location of the given vertex        or other position,    -   where R₁ is the harmonic mean distance of rays cast from the        given vertex or other position,    -   where {circumflex over (n)} is the surface normal of the        selected vertex, and    -   where {circumflex over (n)}₁ is the surface normal of the given        vertex or other position.

And the renderer 23 preferably uses the following equation to computethe error value if more than one vertex or other position is located instep 718, step 730, and/or step 742:$ɛ = \frac{\sum\limits_{i = 1}^{n}\quad ɛ_{i}}{n}$

-   -   where ε is the error value corresponding to the diffusely        reflected light directly computed at each of these vertices or        other positions as a group,    -   where n is a count of the one or more vertices or other        positions located in step 718, step 730, and/or step 742, and    -   where ε_(i) is the error value computed for the diffusely        reflected light directly computed at the i^(th) vertex or other        position in the one or more vertices or other positions located        in step 718, step 730, and/or step 742.

After computing the error value for the one or more vertices or otherpositions located in step 718, step 730, and/or step 742, the renderer23 determines whether the error value is acceptable (step 750). Theactions of the renderer 23 in step 750 are essentially identical tothose of step 726 and step 738. In preferred embodiments, thisdetermination is again made by reference to the predefined errortolerance included in the object scene data and/or the active objectscene data 32. If the error value computed in step 746 is less than thispredefined error tolerance, which may be increased by reference to thecount of located vertices or other positions, the error value isacceptable.

If the error value computed for the one or more vertices or otherpositions located in step 718, step 730, and/or step 742 is acceptable(step 750-Yes), the renderer 23 computes diffusely reflected lightindirectly at the selected vertex (step 770) as described above.

If the error value computed for the one or more vertices or otherpositions located in step 718, step 730 and/or step 742 is unacceptable(step 750-No) or if no vertices or other positions are located in step718, step 730, and step 742 (step 718-No, step 730-No, step 742-No), therenderer 23 determines whether diffusely reflected light has beendirectly computed at one or more surrounding vertices or other positionswithin a distance equal to the predefined constant from the selectedvertex (step 754). The renderer 23 extracts the location of the selectedvertex from the vertices array 150 and uses it to scan the K-D tree forentries that are within a distance that is one half of the predefinedconstant from the selected vertex. Because no vertices or otherpositions were located in step 718, step 730, and step 742 or the errorvalue computed in connection with vertices or other positions that werelocated is unacceptable, the renderer 23 preferably expands the searchvolume. In preferred embodiments of the present invention, vertices orother positions located in step 718, step 730, and/or step 742 do notcount towards the one or more vertices or other positions, if any,located in step 754.

If the renderer 23 determines that diffusely reflected light has beendirectly computed at one or more surrounding vertices or other positionswithin a distance that is equal to the predefined constant from theselected vertex (step 754-Yes), the renderer 23 computes an error valuefor these vertices or other positions (step 758). Step 758 isessentially identical to step 722, step 734, and step 746, except thatthe renderer 23 preferably does not re-compute error values for verticesor other positions, if any, located in step 718, step 730, and/or step742. Instead, the renderer 23 preferably maintains the error valuescomputed for these vertices or other positions in step 718, step 730,and/or step 742 for subsequent use in step 758, if need be. The renderer23 preferably uses the following equation to compute the error value ifonly one vertex or other position in total is located in step 718, step730, step 742, and step 754:${ɛ_{1} = {\frac{{\overset{\rightarrow}{P} - {\overset{\rightarrow}{P}}_{1}}}{R_{1}} + \sqrt{1 - {\hat{n} \cdot {\hat{n}}_{1}}}}},$

-   -   where ε₁ is the error value corresponding to the diffusely        reflected light directly computed at the given vertex or other        position,    -   where {right arrow over (P)} is a location of the selected        vertex,    -   where {right arrow over (P)}₁ is a location of the given vertex        or other position,    -   where R₁ is the harmonic mean distance of rays cast from the        given vertex or other position,    -   where {circumflex over (n)} is the surface normal of the        selected vertex, and    -   where {circumflex over (n)}₁ is the surface normal of the given        vertex or other position.

And the renderer 23 preferably uses the following equation to computethe error value if more than one vertex or other position is located instep 718, step 730, step 742, and/or step 754:$ɛ = \frac{\sum\limits_{i = 1}^{n}\quad ɛ_{i}}{n}$

-   -   where ε is the error value corresponding to the diffusely        reflected light directly computed at each of these vertices or        other positions as a group,    -   where n is a count of the one or more vertices or other        positions located in step 718, step 730, step 742, and/or step        754, and    -   where ε_(l) is the error value computed for the diffusely        reflected light directly computed at the i^(th) vertex or other        position in the one or more vertices or other positions located        in step 718, step 730, step 742, and/or step 754.

After computing the error value for the one or more vertices or otherpositions located in step 718, step 730, step 742, and/or step 754, therenderer 23 determines whether the error value is acceptable (step 762).The actions of the renderer 23 in step 762 are essentially identical tothose of step 726, step 738, and step 750. In preferred embodiments,this determination is again made by reference to the predefined errortolerance included in the object scene data and/or the active objectscene data 32. If the error value computed in step 758 is less than thispredefined error tolerance, which may be increased by reference to thecount of located vertices or other positions, the error value isacceptable.

If the error value computed for the one or more vertices or otherpositions located in step 718, step 730, step 742, and/or step 754 isacceptable (step 762-Yes), the renderer 23 computes diffusely reflectedlight indirectly at the selected vertex (step 770) as described above.

If the error value computed for the one or more vertices or otherpositions located in step 718, step 730, step 742, and/or step 754 isunacceptable (step 762-No) or if no vertices or other positions arelocated in step 718, step 730, step 742, and step 754 (step 718-No, step730-No, step 742-No, step 754-No), the renderer 23 directly computesdiffusely reflected light at the selected vertex directly (step 766).

As noted above, this process includes casting a first set of rays intothe object scene from the selected vertex. If it has not already beencomputed for the same level of recursion, the renderer 23 computesdiffusely reflected light at the intersections of these rays andprimitives in the object scene. In this example, the recursion level ofdiffusely reflected light at the intersections of the first set of raysis one.

Again, computing diffusely reflected light at these intersections mayinclude casting a second set of rays from one or more vertices or otherpositions. In this example, the recursion level of diffusely reflectedlight at the intersections of the second sets of rays is two. Therecursion level increases as additional sets of rays are cast fromvertices or other positions. Typically, the object scene data 21includes an upper recursion level. For example, the object scene data 21may specify that only the first set of rays and one or more second setsof rays may be cast in order to compute diffusely reflected light at avertex or other position.

In preferred embodiments of the present invention, the number of raysincluded in sets of rays cast to compute diffusely reflected light at avertex or other position decreases as the level of recursion increases.As noted above, the need for accuracy is reduced at each level ofrecursion because the overall effect of diffusely reflected light at avertex or other position is reduced at each level of recursion.

Finally, each time a set of rays is cast from an intersection and/or avertex or other position, certain values, in addition to the diffuselyreflected light at the intersection and/or the vertex or other position,are computed and maintained for the intersection and/or the vertex orother position. More specifically, the renderer 23 computes the harmonicmean distance of the rays cast from a given vertex or other position andtwo gradients for the given vertex or other position by reference tothese rays and the contribution of each ray to diffusely reflected lightat the given vertex or other position.

The harmonic mean distance is computed as follows:$R = \frac{n}{\sum\limits_{i = 1}^{n}\quad\frac{1}{a_{i}}}$

-   -   where R is the harmonic mean distance,    -   where n is the count of rays, and    -   where a_(i) is the length of the i^(th) ray.

FIG. 8 illustrates the non-regular processing order described above inconnection with FIG. 7. In this illustration, vertices v142-1, v142-24,v142-15, v142-8, v142-4, and v142-17 are the first six vertices selectedin step 714 of FIG. 7 (this order is merely for illustration, and not alimitation of the present invention. It is possible that because of thedistance between each of these vertices, diffusely reflect light may bedirectly computed for each of these vertices (in this illustration, itis assumed that it is). Regardless of the processing order of theremaining vertices, diffusely reflected light has been directly computedat neighboring vertices in more than one direction from these vertices(this may be especially true if diffusely reflect light has beendirectly computed for vertices or other positions not included in thegrid illustrated in FIG. 8, but that are within a certain distance ofthese vertices). As a result, the indirect computation of diffuselyreflected light at some or all of these other vertices is more accurate.Further, the variance of indirect light from one vertex to the next,whether computed directly or indirectly, is accurately smoother.

As noted above, the step of shading a visibility grid may includecasting rays into the object scene for intersection with shading grids.Determining whether a ray intersects an object may include severalsteps. If a shading grid has been created for a modeled object in anobject scene, the renderer first determines whether the ray intersects abounding box of the primitive corresponding to the object. If so, therenderer 23 determines whether the ray intersects the bounding box ofthe shading grid, which typically requires substantially more processingtime than determining whether the ray intersects the bounding box of theprimitive corresponding to the object. It may be, however, that ashading grid has not yet been created such that determining whether aray intersects a primitive also includes creating a shading grid so thata bounding box for the shading grid can be computed. For this reason, ashading grid may be created before a visibility grid of a correspondingprimitive. In other words, a ray may intersect a primitive before theprimitive is hidden in step 258.

After shading the visibility grid corresponding to the selectedprimitive or portion of a primitive (step 256) or if the visibility gridcorresponding to the selected primitive or portion of a primitive isalready shaded (step 254-Yes), the renderer hides the visibility gridcorresponding to the selected primitive or portion of a primitive (step258). This step typically includes the renderer 23 projecting thevisibility grid onto the image plane and sampling the visibility grid.In other words, the renderer 23 determines elements of the visibilitygrid that are actually visible or contribute color values to one or morepixels. The renderer 23 may use a number of sampling techniques withoutdeparting from the scope of the present invention. For example, therenderer 23 may sample the visibility grid with points, lines, or areas.The renderer 23 may also use area averaging to compute primitivevisibility and colors for pixels.

Additionally, the U.S. patent application Ser. No. 10/177,678 filed onJun. 20, 2002, entitled “SYSTEM AND METHOD OF SIMULATING MOTION BLUREFFICIENTLY,” commonly assigned with the present invention, andincorporated herein by reference, discloses a system and method ofsimulation motion blur efficiently. Elements of this system and methodare used in some embodiments of the present invention during step 258 inparticular. The simulation of motion blur, however, is not a limitationof the present invention.

The result of the hiding step is typically a plurality of color,transparency, and depth values maintained by the renderer 23 in thesample buffers 38. The color values preferably incorporate diffuselyreflected light directly or indirectly computed. These values may or maynot be subsequently overwritten by the renderer 23 following anotherexecution of the hiding step (step 258) in conjunction with othervisibility grids. Such visibility grids may actually be closer to theimage plane 110 than the (current) visibility grid and, therefore,occlude the (current) visibility grid.

After hiding the visibility grid corresponding to the selected primitiveor portion of a primitive, the renderer 23 preferably removes thepointer to the selected primitive or portion of a primitive from itsprimitive bucket 36 (step 260).

The renderer 23 then determines whether the selected primitive orportion of a primitive is still on-screen (step 262). The step ofshading the visibility grid may offset vertices of the visibility gridsuch that it is no longer in the viewing volume. As a result, step 262includes bounding the shaded visibility grid corresponding to theselected primitive or portion of a primitive and determining whether theresulting bounding box is on-screen.

If the renderer 23 determines that the selected primitive or portion ofa primitive is not still on-screen (step 262-No), the renderer 23removes all pointers to the selected primitive or portion of a primitivefrom remaining primitive buckets 36 (step 263, FIG. 2C). But if therenderer 23, for example, also determines in step 262 that the entireprimitive that includes the selected portion is not still on-screen, therenderer 23 may remove all pointers to this primitive from the primitivebuckets 36.

The renderer 23 then preferably culls corresponding visibility gridsfrom the active object scene data 32 (step 264). At the very least, avisibility grid created for the selected primitive or the selectedportion of a primitive is removed. But if the renderer 23 determines instep 262 that the primitive that includes the selected portion is notstill on-screen, the renderer 23 may remove all visibility grids createdfor this primitive.

The renderer 23 then determines whether the selected primitive orportion of a primitive is ray traceable (step 266). If the renderer 23determines that the selected primitive or portion of a primitive is raytraceable (step 226-Yes), the renderer 23 returns to step 208 to selectanother primitive or portion of a primitive. Since the selectedprimitive or portion of a primitive may be intersected by a ray whilethe renderer 23 is shading another primitive, data about the selectedprimitive or portion of a primitive is preferably maintained.

If the renderer 23 determines that the selected primitive or portion ofa primitive is not ray traceable (step 266-No), the renderer 23 cullsdata related to the selected primitive or the primitive that includesthe selected portion from the active object scene data 32 (except, forexample, an indication that the selected primitive or the primitive thatincludes the selected portion has already been processed) (step 268).The renderer 23 then returns to step 208 to select another primitive orportion of a primitive.

If the renderer 23 determines that the selected primitive or portion ofa primitive is still on-screen (step 262-Yes), the renderer 23determines whether the selected primitive or the primitive that includesthe selected portion is referenced in any primitive buckets 36 (step270, FIG. 2D). If not (step 270-No), the renderer 23 culls thevisibility grid created for the selected primitive or the selectedportion of a primitive (step 272).

But if the selected primitive or the primitive that includes theselected portion is referenced in any primitive buckets 36 (step270-Yes) or after executing step 272, the renderer 23 determines whetherthe selected primitive or portion of a primitive is ray traceable (step274). If the renderer 23 determines that the selected primitive orportion of a primitive is ray traceable (step 274-Yes), the renderer 23returns to step 208 to select another primitive or portion of aprimitive. Since the selected primitive or portion of a primitive may beintersected by a ray while the renderer 23 is shading another primitive,data about the selected primitive or portion of a primitive ispreferably maintained.

If the renderer 23 determines that the selected primitive or portion ofa primitive is not ray traceable (step 274-No), the renderer 23 cullsdata related to the selected primitive or the primitive that includesthe selected portion from the active object scene data 32 (except, forexample, an indication that the selected primitive or the primitive thatincludes the selected portion has already been processed) (step 276).The renderer 23 then returns to step 208 to select another primitive orportion of a primitive.

While the present invention has been described with reference to a fewspecific embodiments, the description is illustrative of the inventionand is not to be construed as limiting the invention. Variousmodifications may occur to those skilled in the art without departingfrom the true spirit and scope of the invention as defined by theappended claims.

The present invention can be implemented as a computer program productthat includes a computer program mechanism embedded in a computerreadable storage medium. For instance, the computer program productcould contain the program modules shown in FIG. 1A. These programmodules may be stored on a CD-ROM, magnetic disk storage product, or anyother computer readable data or program storage product. The softwaremodules in the computer program product may also be distributedelectronically, via the Internet or otherwise, by transmission of acomputer data signal (in which the software modules are embedded) on acarrier wave.

1. A method of computing diffusely reflected light at one or morepositions on surfaces in an object scene from object scene data, themethod comprising selecting a non-regular order for processing aplurality of positions on a surface, said plurality of positions havingbeen predetermined; processing the plurality of positions in thenon-regular order, said processing including computing diffuselyreflected light at a position in the plurality of positions by referenceto diffusely reflected light incident on said position when derivingsaid diffusely reflected light at the position by reference to diffuselyreflected light at other positions computed by reference to diffuselyreflected light incident on said other positions is inaccurate; andderiving the diffusely reflected light at the position by reference tothe diffusely reflected light at the other positions computed byreference to diffusely reflected light incident on said other positionswhen said deriving the diffusely reflected light at the position byreference to the diffusely reflected light at the other positions isaccurate.
 2. The method of claim 1, wherein the surface comprises aNURBS; and the plurality of positions correspond to control points ofthe NURBS.
 3. The method of claim 1, wherein the surface is asubdivision surface; and the plurality of positions correspond tovertices of the subdivision surface.
 4. The method of claim 1, whereinthe object comprises a parametric patch; and the plurality of positionscorrespond to control points of the parametric patch.
 5. The method ofclaim 1, wherein the surface comprises a grid of micropolygons; and theplurality of positions correspond to vertices of the grid ofmicropolygons.
 6. The method of claim 1, wherein the non-regular ordercomprises a random order.
 7. The method of claim 1, wherein thenon-regular order comprises a pseudo-random order.
 8. The method ofclaim 1, wherein the non-regular order comprises a quasi-random order.9. The method of claim 1, wherein the selecting comprises creating alist, said list including an entry for each of said plurality ofpositions, a value of each entry equal to a position of said each entryin the list; and shuffling the values of said each entry in the list,said list subsequently in the non-regular order, said list referred toduring the processing step.
 10. The method of claim 1, wherein computingdiffusely reflected light at a position in the plurality of positions byreference to diffusely reflected light incident on said positionincludes casting a ray for the position into the object scene forintersection with an object in the object scene to compute diffuse lightreflected by said object onto said position.
 11. The method of claim 1,wherein determining whether the deriving the diffusely reflected lightat the position by reference to diffusely reflected light at the otherpositions computed by reference to diffusely reflected light incident onsaid other positions is inaccurate includes computing an error value byreference to a location of the position, a location of one of said otherpositions, an average length of rays cast from said location of one ofsaid other positions, a surface normal of said location of the position,and a surface normal of said location of one of said other positions;and comparing the error value to a predefined error tolerance, whereinthe deriving said diffusely reflected light at the position by referenceto diffusely reflected light at other positions computed by reference todiffusely reflected light incident on said other positions is inaccuratewhen said error value is greater than or equal to said predefined errortolerance.
 12. The method of claim 11, further comprising executing saidcomputing an error value step for each of the other positions to producea plurality of error values; adjusting the predefined error tolerance byreference to a count of said other positions, wherein said predefinederror tolerance is increased when the count reaches a predefined value;and comparing an average of said error values to the predefined errortolerance following said adjusting step.
 13. The method of claim 11,wherein the reference to the location of the position, the location ofone of said other positions, the average length of rays cast from saidlocation of one of said other positions, the surface normal of saidlocation of the position, and the surface normal of said location of oneof said other positions takes a form of:${ɛ_{1} = {\frac{{\overset{->}{P} - {\overset{->}{P}}_{1}}}{R_{1}} + \sqrt{1 - {\hat{n} \cdot {\hat{n}}_{1}}}}},$where ε₁ is the error value, where {right arrow over (P)} is thelocation of the position, where {right arrow over (P)}₁ is the locationof one of said other positions, where R₁ is the harmonic mean distanceof rays cast from the location of one of said other positions, where{circumflex over (n)} is the surface normal of the location of theposition, and where {circumflex over (n)}₁ is the surface normal of thelocation of one of said other positions.
 14. The method of claim 1,wherein said deriving the diffusely reflected light at the position byreference to the diffusely reflected light at the other positionscomputed by reference to diffusely reflected light incident on saidother positions includes computing a weighted average of said diffuselyreflected light at the other positions.
 15. The method of claim 14,wherein said computing the weighted average takes a form of:$E = {\sum\limits_{i\Longrightarrow 1}^{n}\quad{ɛ_{i}{\sum\limits_{i\Longrightarrow 1}^{n}\frac{{{{E_{i}\left( {{\hat{n}}_{i} \times \hat{n}} \right)} \cdot {\overset{->}{V}}_{r}}E_{i}} + {{\left( {\overset{->}{P} - {\overset{->}{P}}_{i}} \right) \cdot {\overset{->}{V}}_{t}}E_{i}}}{ɛ_{i}}}}}$where E is the weighted average of said diffusely reflected light atother positions, where ε_(i) is an error value computed for one of saidother positions, where n is a count of said other positions, where E_(i)is diffusely reflected light at said one of said other positions, where{right arrow over (V)}_(r) is a rotational gradient computed inconjunction with E_(i), where {right arrow over (V)}_(i) is atranslational gradient computed in conjunction with E_(i), where {rightarrow over (P)} is a location of the position, where {right arrow over(P)}_(i) is a location of said one of said other positions, where{circumflex over (n)} is a surface normal of the location of theposition, and where {circumflex over (n)}_(i) is a surface normal of thelocation of said one of said other positions.
 16. A computer programproduct for use in conjunction with a computer system, the computerprogram product comprising a computer readable medium and a computerprogram mechanism embedded therein, the computer program mechanismcomprising: a data structure for storing object scene data, said objectscene data describing objects in the object scene; and a programincluding instructions for selecting a non-regular order for processinga plurality of positions on a surface of an object in the object scene,said plurality of positions having been predetermined; instructions forprocessing the plurality of positions in the non-regular order, saidinstructions for processing including instructions for computingdiffusely reflected light at a position in the plurality of positions byreference to diffusely reflected light incident on said position whenderiving said diffusely reflected light at the position by reference todiffusely reflected light at other positions computed by reference todiffusely reflected light incident on said other positions isinaccurate; and instructions for deriving the diffusely reflected lightat the position by reference to the diffusely reflected light at theother positions computed by reference to diffusely reflected lightincident on said other positions when said deriving the diffuselyreflected light at the position by reference to the diffusely reflectedlight at the other positions is accurate.
 17. The computer programproduct of claim 16, wherein the surface comprises a NURBS; and theplurality of positions correspond to control points of the NURBS. 18.The computer program product of claim 16, wherein the surface is asubdivision surface; and the plurality of positions correspond tovertices of the subdivision surface.
 19. The computer program product ofclaim 16, wherein the object comprises a parametric patch; and theplurality of positions correspond to control points of the parametricpatch.
 20. The computer program product of claim 16, wherein the surfacecomprises a grid of micropolygons; and the plurality of positionscorrespond to vertices of the grid of micropolygons.
 21. The computerprogram product of claim 16, wherein the non-regular order comprises arandom order.
 22. The computer program product of claim 16, wherein thenon-regular order comprises a pseudo-random order.
 23. The computerprogram product of claim 16, wherein the non-regular order comprises aquasi-random order.
 24. The computer program product of claim 16,wherein the instructions for selecting comprises instructions forcreating a list, said list including an entry for each of said pluralityof positions, a value of each entry equal to a position of said eachentry in the list; and instructions for shuffling the values of saideach entry in the list, said list subsequently in the non-regular order,said list referred to during the processing step.
 25. The computerprogram product of claim 16, wherein the instructions for computingdiffusely reflected light at a position in the plurality of positions byreference to diffusely reflected light incident on said positionincludes instructions for casting a ray for the position into the objectscene for intersection with an object in the object scene to computediffuse light reflected by said object onto said position.
 26. Thecomputer program product of claim 16, wherein the instructions fordetermining whether the deriving the diffusely reflected light at theposition by reference to diffusely reflected light at the otherpositions computed by reference to diffusely reflected light incident onsaid other positions is inaccurate includes instructions for computingan error value by reference to a location of the position, a location ofone of said other positions, an average length of rays cast from saidlocation of one of said other positions, a surface normal of saidlocation of the position, and a surface normal of said location of oneof said other positions; and instructions for comparing the error valueto a predefined error tolerance, wherein the deriving said diffuselyreflected light at the position by reference to diffusely reflectedlight at other positions computed by reference to diffusely reflectedlight incident on said other positions is inaccurate when said errorvalue is greater than or equal to said predefined error tolerance. 27.The computer program product of claim 11, further comprisinginstructions for executing said computing an error value step for eachof the other positions to produce a plurality of error values;instructions for adjusting the predefined error tolerance by referenceto a count of said other positions, wherein said predefined errortolerance is increased when the count reaches a predefined value; andinstructions for comparing an average of said error values to thepredefined error tolerance following said adjusting step.
 28. Thecomputer program product of claim 16, wherein the instructions forderiving the diffusely reflected light at the position by reference tothe diffusely reflected light at the other positions computed byreference to diffusely reflected light incident on said other positionsincludes instructions for computing a weighted average of said diffuselyreflected light at the other positions.